物理和化學(xué)中的隨機(jī)過程（第3版）

PREFACE TO THE FIRST EDITION
PREFACE TO THE SECOND EDITION
ABBREVIATED REFERENCES
PREFACE TO THE THIRD EDITION
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
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
.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
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
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
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. Artificial boundaries and normal modes
9. Nonlinear one-step processes
VII. CHEMICAL REACTIONS
1. Kinematics of chemical reactions
2. Dynamics of chemical reactions
3. The stationary solution
4. Open systems
5. Unimolecular reactions
6. Collective systems
7. Composite Markov processes
VIII. THE FOKKER-PLANCK EQUATION
1. Introduction
2. Derivation of the Fokker-Planck equation
3. Brownian motion
4. The Rayleigh particle
5. Application to one-step processes
6. The multivariate Fokker-Planck equation
7. Kramers' equation
IX. THE LANGEVIN APPROACH
1. Langevin treatment of Brownian motion
2. Applications
3. Relation to Fokker-Planck equation
4. The Langevin approach
5. Discussion of the Itt--Stratonovich dilemma
6. Non-Gaussian white noise
7. Colored noise
X. THE EXPANSION OF THE MASTER EQUATION
1. Introduction to the expansion
2. General formulation of the expansion method
3. The emergence of the macroscopic law
4. The linear noise approximation
5. Expansion of a multivariate master equation
6. Higher orders
XI. THE DIFFUSION TYPE
1. Master equations of diffusion type
2. Diffusion in an external field
3. Diffusion in an inhomogeneous medium
4. Multivariate diffusion equation
5. The limit of zero fluctua6ons
XII. FIRST-PASSAGE PROBLEMS
I. The absorbing boundary approach
2. The approach through the adjoint equation - Discrete case
3. The approach through the adjoint equation - Continuous case
4. The renewal approach
5. Boundaries of the Smoluchowski equation
6. First passage of non-Markov processes
7. Markov processes with large jumps
XIII. UNSTABLE SYSTEMS
1. The bistable system
2. The escape time
3. Splitting probability
4. Diffusion in more dimensions
5. Critical fluctuations
6. Kramers' escape problem
7. Limit cycles and fluctuations.
XIV. FLUCTUATIONS IN CONTINUOUS SYSTEMS
1. Introduction
2. Diffusion noise
3. The method of compounding moments
4. Fluctuations in phase space density
5. Fluctuations and the Boltzmann equation
XV. THE STATISTICS OF JUMP EVENTS
1. Basic formulae and a simple example
2. Jump events in nonlinear systems
3. Effect of incident photon statistics
4. Effect of incident photon statistics - continued
XVI. STOCHASTIC DIFFERENTIAL EQUATIONS
1. Definitions
2. Heuristic treatment of multiplicative equations
3. The cumulant expansion introduced
4. The general cumulant expansion
5. Nonlinear stochastic differential equations
6. Long correlation times,
XVII. STOCHASTIC BEHAVIOR OF QUANTUM SYSTEMS
1. Quantum probability
2. The damped harmonic oscillator
3. The elimination of the bath,
4. The elimination of the bath - continued
5. The Schr'odinger-Langevin equation and the quantum master equation
6. A new approach to noise
7. Internal noise
SUBJECT INDEX