This course focuses on Modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic...

Topic: probability

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Jul 29, 2022
07/22

by
Downing, Douglas

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xi, 330 pages : 28 cm

Topics: Statistics, Probabilities, Probability, Probabilités, probability

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web

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Probability-Project dumped with WikiTeam tools.

Topics: wiki, wikiteam, wikispaces, Probability-Project, probability-project,...

Title from cover

Topic: PROBABILITY.

London School of Hygiene & Tropical Medicine Library & Archives Service

Topic: Probability

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Mar 1, 2022
03/22

by
Pfeiffer, Paul E

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xiii, 403 pages 25 cm

Topics: Probabilities, Probability, Probabilités, probability, Wahrscheinlichkeitsrechnung

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Jul 25, 2022
07/22

by
Jaynes, E. T. (Edwin T.)

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11, 9, 727 pages : 24 cm

Topics: Probabilities, Probability, Probabilités, probability, Sannolikhetslära

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Oct 6, 2015
10/15

by
Tovey, Craig A.

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Title from cover

Topic: PROBABILITY.

In this paper one generalizes the classical probability and imprecise probability to the notion of “neutrosophic probability” in order to be able to model Heisenberg’s Uncertainty Principle of a particle’s behavior, Schrödinger’s Cat Theory, and the state of bosons which do not obey Pauli’s Exclusion Principle (in quantum physics). Neutrosophic probability is close related to neutrosophic logic and neutrosophic set, and etymologically derived from “neutrosophy”.

Topics: imprecise probability, neutrosophic probability, neutrosophic logic

In this paper one generalizes the classical probability and imprecise probability to the notion of “neutrosophic probability” in order to be able to model Heisenberg’s Uncertainty Principle of a particle’s behavior, Schrödinger’s Cat Theory, and the state of bosons which do not obey Pauli’s Exclusion Principle (in quantum physics). Neutrosophic probability is close related to neutrosophic logic and neutrosophic set, and etymologically derived from “neutrosophy”.

Topics: imprecise probability, neutrosophic probability, neutrosophic logic

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Nov 14, 2013
11/13

by
Charles E. Leiserson

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Abstract: This tutorial teaches dynamic multithreaded algorithms using a Cilk-like [11, 8, 10] model. The material was taught in the MIT undergraduate class 6.046 Introduction to Algorithms as two 80-minute lectures. The style of the lecture notes follows that of the textbook by Cormen, Leiserson, Rivest, and Stein [7], but the pseudocode from that textbook has been �Cilki�ed� to allow it to describe multithreaded algorithms. The �rst lecture teaches the basics behind multithreading,...

Topics: Maths, Statistics and Probability, Probability, Mathematics

Source: http://www.flooved.com/reader/1567

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1 vol. (VIII-410 p.) ; 24 cm

Topics: Probabilities, Probability, Probabilités, probability, Processus stochastiques

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Nov 14, 2013
11/13

by
Erik Demaine

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Topics: Maths, Statistics and Probability, Probability, Mathematics

Source: http://www.flooved.com/reader/1568

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Jun 28, 2018
06/18

by
Sébastien Bubeck; Ewain Gwynne

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Let $d\in\mathbb N$, $\alpha\in\mathbb R$, and let $f :\mathbb R^d\setminus \{0\} \rightarrow (0,\infty)$ be locally Lipschitz and positively homogeneous of degree $\alpha$ (e.g. $f$ could be the $\alpha$th power of a norm on $\mathbb R^d$). We study a generalization of the Eden model on $\mathbb Z^d$ wherein the next edge added to the cluster is chosen from the set of all edges incident to the current cluster with probability proportional to the value of $f$ at the midpoint of this edge,...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1508.05140

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Jun 28, 2018
06/18

by
Ton Viet Ta

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This paper is devoted to studying stochastic parabolic evolution equations with additive noise in Banach spaces of M-type 2. We construct both strict and mild solutions possessing very strong regularities. First, we consider the linear case. We prove existence and uniqueness of strict and mild solutions and show their maximal regularities. Second, we explore the semilinear case. Existence, uniqueness and regularity of mild and strict solutions are shown. Regular dependence of mild solutions on...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1508.07340

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Jun 28, 2018
06/18

by
Olivier Menoukeu Pamen; Dai Taguchi

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In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) $$X_{t}=x_{0}+ \int_{0}^{t} b(s, X_{s}) \mathrm{d}s + L_{t},~x_{0} \in \mathbb{R}^{d},~t \in [0,T],$$ where the drift coefficient $b:[0,T] \times \mathbb{R}^d \to \mathbb{R}^d$ is H\"older continuous in both time and space variables and the noise $L=(L_t)_{0 \leq t \leq T}$ is a $d$-dimensional L\'evy process. We provide the rate of convergence for the Euler-Maruyama approximation when $L$ is...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1508.07513

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Jun 28, 2018
06/18

by
Galina A. Zverkina

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We give a generalization of the ergodic theorem for semi-Markov linear-type processes. This generalization is proved for the case when a common support of distributions defining this process is not arithmetic. Also we give an uniform estimate of expectations of the forward renewal time. These facts are based on the key renewal (Walter Smith's) theorem, and they are very useful in research in the queueing theory.

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1509.06178

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Jun 28, 2018
06/18

by
Marko Raseta

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We prove a strong invariance principle for the sums PN k=1 f(nkx), where f is a smooth periodic function on R and (nk)k?1 is an increasing random sequence. Our results show that in contrast to the classical Salem-Zygmund theory, the asymptotic properties of lacunary series with random gaps can be described very precisely without any assumption on the size of the gaps.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1509.08138

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Jun 28, 2018
06/18

by
Rafik Aguech; Wissem Jedidi

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We give several new characterizations of completely monotone functions and Bernstein functions via two approaches: the first one is driven algebraically via elementary preserving mappings and the second one is developed in terms of the behavior of their restriction on the set of non-negative integers. We give a complete answer to the following question: Can we affirm that a function is completely monotone (resp. a Bernstein function) if we know that the sequence formed by its restriction on the...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1511.08345

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Jun 28, 2018
06/18

by
Anna Aksamit; Monique Jeanblanc; Marek Rutkowski

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We study problems related to the predictable representation property for a progressive enlargement of a reference filtration through observation of a finite random time $\tau$. We focus on cases where the avoidance property and/or the continuity property for martingales in the reference filtration do not hold and the reference filtration is generated by a Poisson process. Our goal is to find out whether the predictable representation property (PRP), which is known to hold in the Poisson...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1512.03992

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Jun 28, 2018
06/18

by
Linan Chen

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This work aims to extend the existing results on thick points of logarithmic-correlated Gaussian Free Fields to Gaussian random fields that are more singular. To be specific, we adopt a sphere averaging regularization to study polynomial-correlated Gaussian Free Fields in higher-than-two dimensions. Under this setting, we introduce the definition of thick points which, heuristically speaking, are points where the value of the Gaussian Free Field is unusually large. We then establish a result on...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1512.07125

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Jun 28, 2018
06/18

by
Alexander Stolyar

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The model is a service system, consisting of several large server pools. A server processing speed and buffer size (which may be finite or infinite) depend on the pool. The input flow of customers is split equally among a fixed number of routers, which must assign customers to the servers immediately upon arrival. We consider an asymptotic regime in which the customer total arrival rate and pool sizes scale to infinity simultaneously, in proportion to a scaling parameter $n$, while the number...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1512.07873

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Jun 29, 2018
06/18

by
Michel Benaïm; Florian Bouguet; Bertrand Cloez

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In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a homogeneous (continuous time) Markov process. Renowned examples such as a bandit algorithms, weighted random walks or decreasing step Euler schemes are included in our framework. Our results are related to functional limit theorems, but the approach differs from the...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1601.06266

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Jun 29, 2018
06/18

by
Yu Gu; Jean-Christophe Mourrat

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We study a generalization of the notion of Gaussian free field (GFF). Although the extension seems minor, we first show that a generalized GFF does not satisfy the spatial Markov property, unless it is a classical GFF. In stochastic homogenization, the scaling limit of the corrector is a possibly generalized GFF described in terms of an "effective fluctuation tensor" that we denote by $\mathsf{Q}$. We prove an expansion of $\mathsf{Q}$ in the regime of small ellipticity ratio. This...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1601.06408

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Jun 29, 2018
06/18

by
Jiajie Wang

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Recent works (Dupire [2005], Cox and Wang [2013], Gassiat et al. [2015]) have studied the construction of Root's embedding. However, all the results so far rely on the assumption that the corresponding stopped process is uniformly integrable, which is equivalent to the potential ordering condition $\mathrm{U}\mu\leq\mathrm{U}\nu$ when the underlying process is a local martingale. In this paper, we study the existence, construction and optimality of Root's embeddings at the absence of the...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1601.07803

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Jun 29, 2018
06/18

by
Levent Onural

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It was shown many times in the literature that a Markov random field is equivalent to a Gibbs random field when all realizations of the field have non-zero probabilities; the proofs are rather complicated. A simpler proof, which is based directly on simple probability theory, is presented. Furthermore, it is shown that the equivalence is still valid when there are constraints (zero probability realizations) of any type. The equivalence extends to infinite size random fields, as well.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1603.01481

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Jun 29, 2018
06/18

by
V Konakov; S Menozzi

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We study the weak error associated with the Euler scheme of non degenerate diffusion processes with non smooth bounded coefficients. Namely, we consider the cases of H{\"o}lder continuous coefficients as well as piecewise smooth drifts with smooth diffusion matrices.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1604.00771

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Jun 29, 2018
06/18

by
Chang-Song Deng; René L. Schilling

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Let $\alpha:[0,1]\to [0,1]$ be a measurable function. It was proved by P. Marchal \cite{Mar15} that the function $$ \phi^{(\alpha)}(\lambda):=\exp\left[ \int_0^1\frac{\lambda-1}{1+(\lambda-1)x}\,\alpha(x)\,d x \right],\quad \lambda>0 $$ is a special Bernstein function. Marchal used this to construct, on a single probability space, a family of regenerative sets $\mathcal R^{(\alpha)}$ such that $\mathcal{R}^{(\alpha)} \stackrel{\text{law}}{=} \overline{\{S^{(\alpha)}_t:t\geq 0\}}$...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1606.04610

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Jun 29, 2018
06/18

by
Jianliang Zhai; Tusheng Zhang; Wuting Zheng

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In this paper, we prove a central limit theorem and estabilish a moderate deviation principle for stochastic models of incompressible second fluids. The weak convergence method inreoduced by [4] plays an important role.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1607.08669

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Jun 29, 2018
06/18

by
Sebastian Engelke; Jevgenijs Ivanovs

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Extreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is crucial and it is typically modeled by a parametric family of spectral distributions. In this work we provide asymptotic bounds on exceedance probabilities that are robust against misspecification of the extremal dependence model. They arise from optimizing...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1608.04214

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Jun 29, 2018
06/18

by
Stephan Gufler

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We show that every exchangeable random semi-ultrametric on the integers can be obtained by sampling an iid sequence from a random marked metric measure space and adding the marks to the distances. We use this representation to define tree-valued Fleming-Viot processes from the $\Xi$-lookdown model. The case with dust is included for processes with values in the space of marked metric measure spaces, and for processes with values in the space of distance matrix distributions.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1608.08074

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Jun 29, 2018
06/18

by
Alexander Veretennikov

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These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as a bridge to the important area of Poisson equations "in the whole space" and with a parameter, the latter theme not being presented here. Why this area is so important was explained in many papers and books (see the references [12, 34, 35]): it...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1610.09661

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Jun 29, 2018
06/18

by
Frederic Cerou; Bernard Delyon; Arnaud Guyader; Mathias Rousset

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The distribution of a Markov process with killing, conditioned to be still alive at a given time, can be approximated by a Fleming-Viot type particle system. In such a system, each particle is simulated independently according to the law of the underlying Markov process, and branches onto another particle at each killing time. The consistency of this method in the large population limit was the subject of several recent articles. In the present paper, we go one step forward and prove a central...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1611.00515

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5.0

Jun 30, 2018
06/18

by
Pierre Monmarché

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A self-interacting velocity jump process is introduced, which behaves in large time similarly to the corresponding self-interacting diffusion, namely the evolution of its normalized occupation measure approaches a deterministic flow.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1701.09065

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Jun 30, 2018
06/18

by
Hiroshi Tsukada

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For symmetric L\'evy processes, if the local times exist, the Tanaka formula has already constructed via the techniques in the potential theory by Salminen and Yor (2007). In this paper, we study the Tanaka formula for arbitrary strictly stable processes with index $\alpha \in (1,2)$ including spectrally positive and negative cases in a framework of It\^o's stochastic calculus. Our approach to the existence of local times for such processes is different from Bertoin (1996).

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1702.00595

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Jun 30, 2018
06/18

by
Ying Hu; Shanjian Tang

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In this paper, we study a scalar linearly growing BSDE with a weakly $L^{1+}$-integrable terminal value. We prove that the BSDE admits a solutionif the terminal value satisfies some $\Psi$-integrability condition, which is weaker than the usual $L^p$ ($p>1$) integrability and stronger than $L\log L$ integrability. We show by a counterexample that $L\log L$ integrability is not sufficient for the existence of solutionto a BSDE of a linearly growing generator.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1704.05212

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Jun 30, 2018
06/18

by
Caio Alves; Rémy Sanchis; Rodrigo Ribeiro

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We propose a random graph model with preferential attachment rule and edge-step functions and prove several properties about it. That is, we consider a random graph model in which at time $t$, a new vertex is added with probability $f(t)$ or a connection between already existing vertices is created with probability $1-f(t)$. All the connections are made according to the preferential attachment rule. To this function of time, $f$, we give the name edge-step function. We investigate the effect of...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1704.08276

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4.0

Jun 29, 2018
06/18

by
Steffen Dereich; Cecile Mailler; Peter Morters

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We study a class of branching processes in which a population consists of immortal individuals equipped with a fitness value. Individuals produce offspring with a rate given by their fitness, and offspring may either belong to the same family, sharing the fitness of their parent, or be founders of new families, with a fitness sampled from a fitness distribution. Examples that can be embedded in this class are stochastic house-of-cards models, urn models with reinforcement, and the preferential...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1601.08128

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Jun 29, 2018
06/18

by
Martynas Manstavicius; Alexander Schnurr

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Using generalized Blumenthal--Getoor indices, we obtain criteria for the finiteness of the $p$-variation of L\'evy-type processes. This class of stochastic processes includes solutions of Skorokhod-type stochastic differential equations (SDEs), certain Feller processes and solutions of L\'evy driven SDEs. The class of processes is wider than in earlier contributions and using fine continuity we are able to handle general measurable subsets of $R^d$ as state spaces. Furthermore, in contrast to...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1602.00942

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Jun 27, 2018
06/18

by
Gunther Leobacher; Michaela Szölgyenyi

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In this paper we introduce a transformation technique, which can on the one hand be used to prove existence and uniqueness for a class of SDEs with discontinuous drift coefficient. One the other hand we present a numerical method based on transforming the Euler-Maruyama scheme for such a class of SDEs. We prove convergence of order $1/2$. Finally, we present numerical examples.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1503.08005

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Jun 27, 2018
06/18

by
Valentina Cammarota; Aimé Lachal

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In this paper, we provide a methodology for computing the probability distribution of sojourn times for a wide class of Markov chains. Our methodology consists in writing out linear systems and matrix equations for generating functions involving relations with entrance times. We apply the developed methodology to some classes of random walks with bounded integer-valued jumps.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1503.08632

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Jun 28, 2018
06/18

by
Antonio Auffinger; Si Tang

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We study the statistics of the largest eigenvalues of $p \times p$ sample covariance matrices $\Sigma_{p,n} = M_{p,n}M_{p,n}^{*}$ when the entries of the $p \times n$ matrix $M_{p,n}$ are sparse and have a distribution with tail $t^{-\alpha}$, $\alpha>0$. On average the number of nonzero entries of $M_{p,n}$ is of order $n^{\mu+1}$, $0 \leq \mu \leq 1$. We prove that in the large $n$ limit, the largest eigenvalues are Poissonian if $\alpha 2(1+\mu^{{-1}})$. We also extend the results of...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1506.06175

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Jun 28, 2018
06/18

by
Tommi Sottinen; Lauri Viitasaari

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We show that every multiparameter Gaussian process with integrable variance function admits a Wiener integral representation of Fredholm type with respect to the Brownian sheet. The Fredholm kernel in the representation can be constructed as the unique symmetric square root of the covariance. We analyze the equivalence of multiparameter Gaussian processes by using the Fredholm representation and show how to construct series expansions for multiparameter Gaussian processes by using the Fredholm...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1506.07211

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Jun 28, 2018
06/18

by
Sandra Palau; Juan Carlos Pardo

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We consider continuous state branching processes that are perturbed by a Brownian motion. These processes are constructed as the unique strong solution of a stochastic differential equation. The long-term extinction and explosion behaviours are studied. In the stable case, the extinction and explosion probabilities are given explicitly. We find three regimes for the asymptotic behaviour of the explosion probability and, as in the case of branching processes in random environment, we find five...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1506.09197

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Jun 28, 2018
06/18

by
Anita Behme; Lennart Bondesson

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Let $ k >0 $ be an integer and $ Y $ a standard Gamma$(k)$ distributed random variable. Let $ X $ be an independent positive random variable with a density that is hyperbolically monotone (HM) of order $ k.$ Then $Y\cdot X$ and $Y/X $ both have distributions that are generalized gamma convolutions (GGCs). This result extends a result of Roynette et al. from 2009 who treated the case $ k=1 $ but without use of the HM-concept. Applications in excursion theory of diffusions and in the theory of...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1507.04017

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Jun 28, 2018
06/18

by
Emilio De Santis; Mauro Piccioni

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In this paper we study stochastic process indexed by $\mathbb {Z}$ constructed from certain transition kernels depending on the whole past. These kernels prescribe that, at any time, the current state is selected by looking only at a previous random instant. We characterize uniqueness in terms of simple concepts concerning families of stochastic matrices, generalizing the results previously obtained in De Santis and Piccioni (J. Stat. Phys., 150(6):1017--1029, 2013).

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1508.00867

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Jun 28, 2018
06/18

by
Andrey Sarantsev

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Consider an multidimensional obliquely reflected Brownian motion in the positive orthant, or, more generally, in a convex polyhedral cone. We find sufficient conditions for existence of a stationary distribution and convergence to this distribution at the exponential rate, as time goes to infinity. We also prove that certain exponential moments for this distribution are finite, thus providing a tail estimate for this distribution. Finally, we apply these results to systems of rank-based...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1509.01781

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Jun 28, 2018
06/18

by
Ran Wei

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We study the long-range directed polymer model on $\mathbbm{Z}$ in a random environment, where the underlying random walk lies in the domain of attraction of an $\alpha$-stable process for some $\alpha\in(0,2]$. Similar to the more classic nearest-neighbor directed polymer model, as the inverse temperature $\beta$ increases, the model undergoes a transition from a weak disorder regime to a strong disorder regime. We extend most of the important results known for the nearest-neighbor directed...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1510.02593

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Jun 28, 2018
06/18

by
Phil Kopel

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We prove that, for general test functions, the limiting behavior of the linear statistic of an independent entry random matrix is determined only by the first four moments of the entry distributions. This immediately generalizes the known central limit theorem for independent entry matrices with complex normal entries. We also establish two central limit theorems for matrices with real normal entries, considering separately functions supported exclusively on and exclusively away from the real...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1510.02987

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Jun 28, 2018
06/18

by
Jean-François Marckert

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Pick $n$ points $Z_0,...,Z_{n-1}$ uniformly and independently at random in a compact convex set $H$ with non empty interior of the plane, and let $Q^n_H$ be the probability that the $Z_i$'s are the vertices of a convex polygon. Blaschke 1917 \cite{Bla} proved that $Q^4_T\leq Q^4_H\leq Q^4_D$, where $D$ is a disk and $T$ a triangle. In the present paper we prove $Q^5_T\leq Q^5_H\leq Q^5_D$. One of the main ingredients of our approach is a new formula for $Q^n_H$ which permits to prove that...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1511.03658