Handbook of Brownian Motion - Facts and Formulae
There are two parts in this book. The first part is devoted mainly to the properties 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.
1101510860
Handbook of Brownian Motion - Facts and Formulae
There are two parts in this book. The first part is devoted mainly to the properties 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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Handbook of Brownian Motion - Facts and Formulae

Handbook of Brownian Motion - Facts and Formulae

Handbook of Brownian Motion - Facts and Formulae

Handbook of Brownian Motion - Facts and Formulae

Overview

There are two parts in this book. The first part is devoted mainly to the properties 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.

Product Details

ISBN-13: 9783034894623
Publisher: Birkhäuser Basel
Publication date: 10/23/2012
Series: Probability and Its Applications
Edition description: 2nd ed. 2002
Pages: 685
Product dimensions: 6.10(w) x 9.25(h) x 0.05(d)

Table of Contents

I: Theory.- I. Shastic processes in general.- II. Linear diffusions.- III. Shastic calculus.- IV. Brownian motion.- V. Local time as a Markov process.- VI. Differential systems associated to Brownian motion.- Appendix 1. Briefly on some diffusions.- II: TABLES OF DISTRIBUTIONS OF FUNCTIONALS OF BROWNIAN MOTION AND RELATED PROCESSES.- 1. Brownian motion.- 2. Brownian motion with drift.- 3. Reflecting Brownian motion.- 4. Bessel process of order—.- 5. Bessel process of order 1/2.- 6. Bessel process of order zero.- 7. Ornstein-Uhlenbeck process.- 8. Radial Ornstein-Uhlenbeck process.- 9. Geometric Brownian motion.- Appendix 2. Special functions.- Appendix 3. Inverse Laplace transforms.- Appendix 4. Differential equations and their solutions.- Appendix 5. Formulae for n-fold differentiation.
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