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Stochastic methods. A handbook for the natural and social sciences. 4th revised and augmented ed. (English) Zbl 1181.60001
Springer Series in Synergetics. Berlin: Springer (ISBN 978-3-540-70712-7/hbk; 978-3-642-08962-6/pbk). xvii, 447 p. (2009).
Although originally conceived as a book for physicists, chemists and similar scientists, Stochastic Methods has developed a readership with far more varied tastes, and this new edition is designed to cater better for the wider readership, as well as to those the author originally had in mind. This fourth edition of the classic text A Handbook of Stochastic Methods has been significantly augmented, thoroughly revised, and restructured to accomodate the new material within a systematic logical framework. This new revised and augmented edition adheres the original aim: “to make available in simple language and deductive form, the many formulae and methods that can be found in the literature on stochastic methods”.
A new chapter on the applications of stochastic methods in finance provides an introduction to this field using the same simple kind of language as the other parts of the book. This chapter also includes an introduction to Lévy processes, which have found to be very useful in simulating financial systems where more accuracy is required than is available from simple Brownian motion models. New material is also provided on the Itô calculus and stochastic differential equations, on the approach to the white noise limit, on the applications of Poisson representation methods to population dynamics, and on several other applications of stochastic methods.
The reviews on the previous editions can be found at: Zbl 1143.60001 (3rd ed., 2004), Zbl 0934.60003 (5th printing of the 2nd ed., 1998), Zbl 0713.60076 (2nd ed., 1985), Zbl 0515.60002 (1st ed., 1983).

60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60Hxx Stochastic analysis
60Jxx Markov processes
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
00A69 General applied mathematics