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Handbook of Stochastic Methods

C.W. Gardiner

This book is ideal, for people that need a clear introduction to stochastic mathematics and their applications in physical sciences. It is also an excellent reference book, covering a wide range of applications. A graduate student in a mathematical subject should be comfortable with the required background knowledge. The author does state that this book is not intended to be mathematically rigorous in the sense of formal proofs. However the central concepts are well explained and equations are clear, avoiding obscure notations. Though there is no chapter explicitly dedicated to financial mathematics, the book extensively covers Ito Calculus.

The book begins by giving some historical motivation to the subject and revises the central ideas of probability theory. A chapter on Markov processes introduces the Chapman-Kolmogorov equation and the Master equation and guides the reader towards stochastic differential equations. What follows are two excellent chapters on stochastic calculus and on applying the Fokker Planck equation. The second part of the book explores jump and diffusion processes in more detail and the approximation methods required to solve problems. The book ends with a chapter on describing quantum systems that are affected by the stochastic nature of thermal effects.

In summary an excellent self study and reference book on stochastic methods.

Reviewed by Raffaello Vardavas. Click here to buy this book at Amazon.co.uk.

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