{About the first edition: To sum it up, one can perhaps see a distinction among advanced probability books into those which are original and pathbreaking in content, such as Levy's and Doob's wellknown examples, and those which aim primarily to…
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{A new look at weakconvergence methods in metric spacesfrom a master of probability theory In this new edition, Patrick Billingsley updates his classic work Convergence of Probability Measures to reflect developments of the past thirty years.…

This book began as lecture notes for an advanced graduate course called Probability on Trees that Lyons gave in Spring 1993. We are grateful to Rabi Bhattacharya for having suggested that he teach such a course. We have attempted to preserve the…

We are developing a dual panel breastdedicated PET system using LSO scintillators coupled to position sensitive avalanche photodiodes (PSAPD). The charge output is amplified and read using NOVA RENA3 ASICs. This paper shows that the coincidence…

This article presents a simple yet powerful new approach for approximating the value of American options by simulation. The key to this approach is the use of least squares to estimate the conditional expected payoff to the optionholder from…

From the reviews: "This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the…

The ddimensional Gaussian free field (GFF), also called the (Euclidean bosonic) massless free field, is a ddimensionaltime analog of Brownian motion. Just as Brownian motion is the limit of the simple random walk (when time and space are…

This tutorial discusses the ExpectationMaximization (EM) algorithm of Demp ster, Laird and Rubin 1. The approach taken follows that of an unpublished note by Stuart Russel, but fleshes out some of the gory details. In order to ensure that the…

This classic textbook, now reissued, offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The new edition has been made even more selfcontained than before; it…

This is a masterly introduction to the modern and rigorous theory of probability. The author adopts the martingale theory as his main theme and moves at a lively pace through the subject's rigorous foundations. Measure theory is introduced and then…

It has been 13 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications,…

We consider the problem of assigning transition probabilities to the edges of a path, so the resulting Markov chain or random walk mixes as rapidly as possible. In this note we prove that fastest mixing is obtained when each edge has a transition…

The first draft of these notes was prepared by the students in Math 735 at the University of Wisconsin  Madison during the fall semester of 1992. The students faithfully transcribed many of the errors made by the lecturer. While the notes have been…

For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired…

These lecturenotes are based on a couple of seminartalks I gave at Courant \nin Spring 2001. I am extremely grateful to Prof. S.R.S. Varadhan for supporting \nand stimulating my interest in Malliavin Calculus. I am also indepted to Nicolas…

A tempered stable Lévy process combines both the αstable and Gaussian trends. In a short time frame it is close to an αstable process while in a long time frame it approximates a Brownian motion. In this paper we consider a general and robust…

In this article, we show how the theory of rough paths can be used to provide a notion of solution to a class of nonlinear stochastic PDEs of Burgers type that exhibit toohigh spatial roughness for classical analytical methods to apply. In fact,…

Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other selforganizing systems. Ordinarily, the…

Introduction This is a concise summary of recommended features in LATEX and a couple of extension packages for writing math formulas. Readers needing greater depth of detail are referred to the sources listed in the bibliography, especially…

This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby…
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