Stochastic Methods: A Handbook for the Natural and Social Sciences / Edition 4

by Crispin Gardiner

Overview

This fourth edition of Shastic Methods is thoroughly revised and augmented, and has been completely reset. While keeping to the spirit of the book I wrote originally, I have reorganised the chapters of Fokker-Planck equations and those on approximation methods, and introduced new material on the white noise limit of driven shastic systems, and on applications and validity of simulation methods based on the Poisson representation. Further, in response to the revolution in financial markets following from the discovery by Fischer Black and Myron Scholes of a reliable option pricing formula, I have written a chapter on the application of shastic methods to financial markets. In doing this, I have not restricted myself to the geometric Brownian motion model, but have also attempted to give some favour of the kinds of methods used to take account of the realities of financial markets. This means that I have also given a treatment of Levy processes and their applications to finance, since these are central to most current thinking. Since this book was written the rigorous mathematical formulation of shastic processes has developed considerably, most particularly towards greater precision and generality, and this has been reflected in the way the subject is presented in modern applications, particularly in finance.

Product Details

ISBN-13:	9783642089626
Publisher:	Springer Berlin Heidelberg
Publication date:	11/19/2010
Series:	Springer Series in Synergetics , #13
Edition description:	Fourth Edition 2009
Pages:	447
Product dimensions:	6.10(w) x 9.10(h) x 1.10(d)

Table of Contents

A Historical Introduction.- Probability Concepts.- Markov Processes.- The Ito Calculus and Shastic Differential Equations.- The Fokker-Planck Equation.- The Fokker-Planck Equation in Several Dimensions.- Small Noise Approximations for Diffusion Processes.- The White Noise Limit.- Beyond the White Noise Limit.- Lévy Processes and Financial Applications.- Master Equations and Jump Processes.- The Poisson Representation.- Spatially Distributed Systems.- Bistability, Metastability, and Escape Problems.- Simulation of Shastic Differential Equations.

Editorial Reviews

From the reviews of the fourth edition:

“This is the fourth edition of a textbook intended for everyone interested in practising shastic processes. … this fourth one is ‘thoroughly revised and augmented, and has been completely reset. … this new edition is designed to cater better for the wider readership as well as to those [he] originally had in mind’. … The bibliography is well presented, with a list of the references cited in each chapter, a commented global bibliography and an author index.” (Yves Elskens, Belgian Physical Society Magazine, Issue 2, 2012)

From the Publisher