Probability and Its Applications

By: Andrei N. Borodin, Paavo Salminen

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Hardcover | 1 May 2002 | Edition Number 2

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Hardcover
704 Pages

Edition Type
Revised

Dimensions(cm)
23.5 x 16.51 x 3.18

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There are two parts in this book. The first part is devoted mainly to the proper- ties of linear diffusions in general and Brownian motion in particular. The second part consists of tables of distributions of functionals of Brownian motion and re- lated processes. The primary aim of this book is to give an easy reference to a large number of facts and formulae associated to Brownian motion. We have tried to do this in a "handbook-style". By this we mean that results are given without proofs but are equipped with a reference where a proof or a derivation can be found. It is our belief and experience that such a material would be very much welcome by students and people working with applications of diffusions and Brownian motion. In discussions with many of our colleagues we have found that they share this point of view. Our original plan included more things than we were able to realize. It turned out very soon when trying to put the plan into practice that the material would be too wide to be published under one cover. Excursion theory, which most of the recent results concerning linear Brownian motion and diffusions can be classified as, is only touched upon slightly here, not to mention Brownian motion in several dimensions which enters only through the discussion of Bessel processes. On the other hand, much attention is given to the theory of local time.

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Non-Fiction Science Chemistry Mathematics Probability & Statistics Applied Mathematics Stochastics

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Published: 23rd October 2012

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Preface to the First edition
Preface to the second edition
Notation
Theory
Stochastic processes in general	p. 1
Linear diffusions	p. 12
Stochastic calculus	p. 38
Brownian motion	p. 51
Local time as a Markov process	p. 81
Differential systems associated to Brownian motion	p. 103
App. 1: Briefly on some diffusions	p. 119
Tables of Distributions of Functionals of Brownian Motion and Related Processes
Introduction	p. 145
Brownian motion	p. 153
Brownian motion with drift	p. 250
Reflecting Brownian motion	p. 333
Bessel process of order [upsilon]	p. 373
Bessel process of order 1/2	p. 429
Bessel process of order zero	p. 507
Ornstein-Uhlenbeck process	p. 522
Radial Ornstein-Uhlenbeck process	p. 565
Geometric Brownian motion	p. 606
Special functions	p. 637
Inverse Laplace transforms	p. 649
Differential equations and their solutions	p. 652
Formulae for n-fold differentiation	p. 657
Bibliography	p. 659
Subject index	p. 669
Table of Contents provided by Blackwell. All Rights Reserved.

Probability and Its Applications

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Hardcover

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Other Editions and Formats

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