The Fokker-Planck equation. Methods of solution and applications. 2nd ed. (English) Zbl 0665.60084

Springer Series in Synergetics, 18. Berlin etc.: Springer-Verlag. xiv, 472 p. DM 98.00 (1989).
This is a practitioners oriented textbook, which is rather classical in its presentation, i.e. no martingales, stochastic calculus and all that; but quite up to date in the applications chosen to illustrate the theory. The material is well organized, going from motivations to basic theory to applications. The basic theory consists of a study of the basic processes (in the physicists way) and of an analysis of the Fokker-Planck equation (which describes the time evolution of the transition probability density of the processes under study).
Much emphasis is put on the different methods to obtain approximate solutions. Quite a number are developed in the context of the different applications which are discussed. A long and comprehensive bibliography is included.
Reviewer: H.Gzyl


60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
60J65 Brownian motion