Handbook of stochastic methods for physics, chemistry and the natural sciences. Corrected printing of the 2nd ed. 1985. (English) Zbl 0713.60076
Springer Series in Synergetics, 13. Berlin etc.: Springer-Verlag. xix, 442 p. DM 99.00 (1990).
[For the 1st ed. (1983) see Zbl 0515.60002.]
This book is intended for users having to employ diffusion or birth and death processes to analyze phenomenological models.
The material is developed in an orderly fashion, starting from the very basics, after which the fundamental evolution equations for the transition probabilities are obtained. Then a simplified version of stochastic integration is given and stochastic differential equations are described. This covers the first four chapters.
The next two chapters deal with various aspects of the Fokker-Planck equation, covering methods of obtaining exact and approximate solutions, boundary analysis, different asymptotics. They are well sprinkled with applications.
Chapters 7 and 8 deal with processes having countable state spaces (populations or particles moving in lattices). When the need for continuous state space appears, a discretization process is invoked. Actually, appropriate use of measure theoretic notation would make possible to deal with processes moving by jumps in any (reasonable) state space. The applications now comprise models for chemical reactions and transport equations.
The following chapter is devoted to another topic related to phenomenological description of chemically reacting systems. Here a particle making transitions between potential as well as by the action of noise is described. Since the contents of chapter 10 cannot be described in few words, I do not comment on it.
The book is suitable for an introductory graduate course on the subject for natural sciences students.
This book is intended for users having to employ diffusion or birth and death processes to analyze phenomenological models.
The material is developed in an orderly fashion, starting from the very basics, after which the fundamental evolution equations for the transition probabilities are obtained. Then a simplified version of stochastic integration is given and stochastic differential equations are described. This covers the first four chapters.
The next two chapters deal with various aspects of the Fokker-Planck equation, covering methods of obtaining exact and approximate solutions, boundary analysis, different asymptotics. They are well sprinkled with applications.
Chapters 7 and 8 deal with processes having countable state spaces (populations or particles moving in lattices). When the need for continuous state space appears, a discretization process is invoked. Actually, appropriate use of measure theoretic notation would make possible to deal with processes moving by jumps in any (reasonable) state space. The applications now comprise models for chemical reactions and transport equations.
The following chapter is devoted to another topic related to phenomenological description of chemically reacting systems. Here a particle making transitions between potential as well as by the action of noise is described. Since the contents of chapter 10 cannot be described in few words, I do not comment on it.
The book is suitable for an introductory graduate course on the subject for natural sciences students.
Reviewer: H.Gzyl
MSC:
| 60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |
| 00A69 | General applied mathematics |
| 60Hxx | Stochastic analysis |
| 60Jxx | Markov processes |
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
