Stochastic Processes in Physics and ChemistryThe third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations. Apart from that throughout the text corrections have been made and a number of references to later developments have been included. From the recent textbooks the following are the most relevant. 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)

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Contents
1  
30  
Chapter III STOCHASTIC PROCESSES  52 
Chapter IV MARKOV PROCESSES  73 
Chapter V THE MASTER EQUATION  96 
Chapter VI ONESTEP PROCESSES  134 
Chapter VII CHEMICAL REACTIONS  166 
Chapter VIII THE FOKKERPLANCK EQUATION  193 
Chapter XI THE DIFFUSION TYPE  273 
Chapter XII FIRSTPASSAGE PROBLEMS  292 
Chapter XIII UNSTABLE SYSTEMS  326 
Chapter XIV FLUCTUATIONS IN CONTINUOUS SYSTEMS  363 
Chapter XV THE STATISTICS OF JUMP EVENTS  383 
Chapter XVI STOCHASTIC DIFFERENTIAL EQUATIONS  396 
Chapter XVII STOCHASTIC BEHAVIOR OF QUANTUM SYSTEMS  422 
457  
Common terms and phrases
absorbing boundary approximation autocorrelation function average boundary condition Brownian particle characteristic function chemical reaction coefficients collision compute Consider constant cumulants defined density matrix Derive described detailed balance determined differential equation diffusion dots eigenvalues energy ensemble equilibrium example Exercise expansion explicitly expression factor Find finite fluctuations Fokker–Planck equation Gaussian given Hence independent initial condition initial value integral interval jump Langevin equation limit Mequation macroscopic equation macrostate Markov process Markovian master equation matrix mean firstpassage molecules moments N.G. van Kampen nonlinear obeys obtained onestep process operator order Q oscillator photons Phys physical Poisson distribution possible potential probability density probability distribution problem properties Qexpansion quantity random walk result Show solved space stationary distribution stationary solution statistical mechanics stochastic differential equation stochastic process Suppose tion transformation transition probability vanishes variables vector velocity Wiener process write zero
Popular passages
Page vii  Que nous sertil d'avoir la panse pleine de viande, si elle ne se digère? si elle ne se transforme en nous? si elle ne nous augmente et fortifie...
Page vii  The interest in fluctuations and in the stochastic method for describing them has grown enormously in the last few decades. The number of articles scattered in the literature of various disciplines must run to thousands and special journals are devoted to the subject. Yet the physicist or chemist who wants to become acquainted with the field cannot easily find a suitable introduction. This book is an attempt to fill this gap in the literature. The first part consists of an introductory exposition...
Page vii  ... enormously in the last few decades. The number of articles scattered in the literature of various disciplines must run to thousands and special journals are devoted to the subject. Yet the physicist or chemist who wants to become acquainted with the field cannot easily find a suitable introduction. This book is an attempt to fill this gap in the literature. The first part consists of an introductory exposition of probability, random events, and stochastic processes as they occur in physics, chemistry...
Page x  An Introduction to Probability Theory and its Applications. Vol. I, 2nd Edition. Wiley, New York.
Page x  Topics in the THeory of Random Noise", Vol. I., RA Silverman, tr., Gordon and Breach, New York, 1963, Ch.