Front Cover -- Stochastic Processes in Physics and Chemistry -- Copyright Page -- TABLE OF CONTENTS -- 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. Artificial boundaries and normal modes -- 9. Nonlinear one-step processes -- Chapter 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 -- Chapter 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-PIanck equation -- 7. Kramers' equation -- Chapter 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 Itô-Stratonovich dilemma -- 6. Non-Gaussian white noise -- 7. Colored noise -- Chapter 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 -- Chapter XI. THE DIFFUSION TYPE -- 1. Master equations of diffusion type -- 2. Diffusion in an external field -- 3. Diffusion in an inhomogeneous medium -- 4. Muitivariate diffusion equation -- 5. The limit of zero fluctuations -- Chapter XII. FIRST-PASSAGE PROBLEMS -- 1. 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 -- Chapter 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 -- Chapter 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 -- Chapter 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 -- Chapter 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 -- Chapter 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 Schrödinger-Langevin equation and the quantum master equation -- 6. A new approach to noise -- 7. Internal noise -- SUBJECT INDEX.