## Description

C.W.Gardiner, Quantum Optics (Springer, Berlin 1991) D.T. Gillespie, Markov Processes (Academic Press, San Diego 1992) W.T. Coffey, Yu.P.Kalmykov, and J.T.Waldron, The Langevin Equation (2nd edition, World Scientific, 2004)

### Key Features

### Readership

## Table of Contents

Dedication

PREFACE TO THE FIRST EDITION

PREFACE TO THE SECOND EDITION

ABBREVIATED REFERENCES

PREFACE TO THE THIRD EDITION

Chapter I: STOCHASTIC VARIABLES

1 Definition

2 Averages

3 Multivariate distributions

4 Addition of stochastic variables

5 Transformation of variables

6 The Gaussian distribution

7 The central limit theorem

Chapter II: RANDOM EVENTS

1 Definition

2 The Poisson distribution

3 Alternative description of random events

4 The inverse formula

5 The correlation functions

6 Waiting times

7 Factorial correlation functions

Chapter III: STOCHASTIC PROCESSES

1 Definition

2 Stochastic processes in physics

3 Fourier transformation of stationary processes

4 The hierarchy of distribution functions

5 The vibrating string and random fields

6 Branching processes

Chapter IV: MARKOV PROCESSES

1 The Markov property

2 The Chapman–Kolmogorov equation

3 Stationary Markov processes

4 The extraction of a subensemble

5 Markov chains

6 The decay process

Chapter V: THE MASTER EQUATION

1 Derivation

2 The class of W-matrices

3 The long-time limit

4 Closed, isolated, physical systems

5 The increase of entropy

6 Proof of detailed balance

7 Expansion in eigenfunctions

8 The macroscopic equation

9 The adjoint equation

10 Other equations related to the master equation

Chapter VI: ONE-STEP PROCESSES

1 Definition; the Poisson process

2 Random walk with continuous time

3 General properties of one-step processes

4 Examples of linear one-step processes

5 Natural boundaries

6 Solution of linear one-step processes with natural boundaries

7 Artificial boundaries

8 A

## Details

- No. of pages:
- 464

- Language:
- English

- Copyright:
- © 2007

- Published:
- 21st March 2007

- Imprint:
- North Holland

- Print ISBN:
- 9780444529657

- Electronic ISBN:
- 9780080475363