Curiculum Vitae
Other Writings
Book reviews
from the
Dutch Mathematical
Book reviews
from the journal
Acta Applicandae

Book review

Author(s) Skorohod, A.V.
Title Stochastic Equations for Complex Systems
Publisher D. Reidel Publishing Company
Year of publication 1988
Reviewed by Viorica-Cerasela Postolache

When the variation of some parameters from a given equation has probabilistic nature say we have a stochastic equation. Stochastic Equations often arise in many fields of science and engineering like as analysis of mechanical structures, biology, physics, chemistry and so on. This book will be of interest to workers in these fields.

The book has been written in order to include a systematic study of so-called stochastic differential equations connected with Markov processes (quasi-diffusion processes) and of some systems consisting of a large number of randomly interacting particles (in the limit results the Brownian motion). The book is accessible to some readers in applied probability theory and applied physics or chemistry. Providing original researches, the book deals with continuous Markov processes in a locally compact space and stochastic equations as well as randomly interacting systems of particles. Applications from the diffusion processes are given. Equations for quasi-diffusion processes are established and solutions of them are obtained. The book includes complete proofs of the main results.

I can say the book is well produced despite some graphical omissions of this edition (on the page xii there exists "the word" obtianed, on the page 132, for example, is possible to write the equations using a little less rows, throughout the book the equations are not sufficiently space between their rows (see for example 163) a.o.). There exists a table of index (subject index) and a comprehensive bibliography.

Generally, the presentation is rigorous and reflects the experience of the author in the research work. The author's aim is to present new researchers in applied stochastic equations for complex systems. Since this topic is relevant in engineering as well as in various life and social sciences, I expect that this book will be of interest to workers in these fields. Also I recommend this book to advanced undergraduate and postgraduate students in physics, medicine, engineering and mathematics. A knowledge of calculus is assumed.