{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.…

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…

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…

These notes are based on a series of lectures given first at the University of Warwick in spring 2008 and then at the Courant Institute in spring 2009. It is an attempt to give a reasonably selfcontained presentation of the basic theory of…

TThis book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of…

Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book provides the reader with comprehensive basic knowledge of Lévy processes, and at the same…

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…

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…

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…

Mycotoxins are small (MW approximately 700), toxic chemical products formed as secondary metabolites by a few fungal species that readily colonise crops and contaminate them with toxins in the field or after harvest. Ochratoxins and Aflatoxins are…

The main purpose of this book is to give a systematic treatment of the theory of stochastic differential equations and stochastic flow of diffeomorphisms, and through the former to study the properties of stochastic flows. The classical theory was…

Choosing good problems is essential for being a good scientist. But what is a good problem, and how do you choose one? The subject is not usually discussed explicitly within our profession. Scientists are expected to be smart enough to figure it out…

Investigators have modeled oceanic and atmospheric vortices in the laboratory in a number of different ways, employing background rotation, density effects, and geometrical confinement. In this article, we address barotropic vortices in a rotating…

Despite application of cryogen spray (CS) precooling, customary treatment of port wine stain (PWS) birthmarks with a single laser pulse does not result in complete lesion blanching for a majority of patients. One obvious reason is nonselective…

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…

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…

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…

When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and…

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…
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