{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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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…

The Akzo Nobel research laboratories formulated this problem in their study of the penetration of radiolabeled antibodies into a tissue that has been infected by a tumor. This study was carried out for diagnostic as well as therapeutic purposes.…

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 book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics,…

This book is an introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results…

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 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,…

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…

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…

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…

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 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…

For this second edition, the text has been thoroughly revised and expanded.

Probability and Measure Theory, Second Edition, is a text for a graduatelevel course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of…

Note onWebers parabolic cylinder functionDn(z) and its associated equations (functional&differential)

We suggest a governing equation that describes the process of polymerchain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the translocated number…

Market smiles and skews are usually managed by using local volatility models a la Dupire. We discover that the dynamics of the market smile predicted by local vol models is opposite of observed market behavior: when the price of the underlying…
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