The handbook covers systematically and in simple language the foundations of Markov systems, stochastic differential equations, Fokker-Planck equations, approximation methods, chemical master equations and quantum-mechanical Markov processes. Strong emphasis is placed on systematic approximation methods for solving problems. Stochastic adiabatic elimination is newly formulated. The book contains the 'folklore' of stochastic methods in systematic form, and is suitable for use as a reference work. In this second edition extra material has been added with recent progress in stochastic methods taken into account.

In the third edition of this classic the chapter on quantum Marcov processes has been replaced by a chapter on numerical treatment of stochastic differential equations to make the book even more valuable for practitioners.

In the third edition of this classic the chapter on quantum Marcov processes has been replaced by a chapter on numerical treatment of stochastic differential equations to make the book even more valuable for practitioners.

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.