Book,
Stochastic processes in physics and chemistry
North Holland, (2007)
Abstract
Of late there is an increasing interest in fluctuating phenomena and stochastic methods describing them, and the present book is an attempt to consolidate such efforts. The book consists of 14 chapters and can be conveniently divided into four parts. Part I consists of 1. Stochastic variables, 2. Random events, 3. Stochastic processes and 4. Markov processes; Part II comprises 5. The master equation, 6. One-step processes, 7. Chemical reactions, and 8. The Fokker-Planck equations and Langevin equations; Part III contains 9. The expansion of the master equation, 10. The diffusion type, and 11. Unstable systems; Part IV deals with diverse topics: 12. Fluctuation in continuous systems, 13. Statistics of jump events, and 14. Stochastic differential equations.
The earliest work on stochastic processes with special reference to problems of physical sciences dates back to 1943, namely, Chandrasekhar's classic review article. There were practically no books written in this flavour until the decade commencing from 1960, by which time the use of stochastic processes had become very popular. Many books have appeared in print since then. The book under review is distinctively different from the existing ones in content and more particularly in the basic approach. Part I covers material of a classical type; even there the approach is very stimulating and a graduate student, particularly in physics or chemistry, will profit enormously by studying the material and working out the problems indicated here and there. Parts II and III cover a good amount of the work of the author himself and it is here that even specialists in the subject will find it worthwhile to read through. The topics treated in Part IV take the reader to the very specialized areas in the frontier of research. Discussions of some topics like statistics of jump events and stochastic differential equations are rather incomplete. The author would have done well to bring them to the same level as the rest of the book. For instance, the use of stochastic calculi in modeling is a significant omission. Likewise, the statistics of jump events could have been improved to include a full discussion on the response phenomena.
On the whole the reviewer found the book most enjoyable and the book can be recommended to applied probabilists, physicists and physical chemists. The graduate student, especially the one who aspires to do modeling in physical sciences, will find the book very inspiring.
