Stochastic Methods: A Handbook for the Natural and Social Sciences

ISBN-13: 9783540707127 / Angielski / Twarda / 2009 / 468 str.

Crispin Gardiner

Opis

This fourth edition of Stochastic 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 appr- imation methods, and introduced new material on the white noise limit of driven stochastic systems, and on applications and validity of simulation methods based on the Poisson representation. Further, in response to the revolution in ?nancial m- kets 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 stochastic me- ods to ?nancial markets. In doing this, I have not restricted myself to the geometric Brownian motion model, but have also attempted to give some ?avour of the kinds of methods used to take account of the realities of ?nancial markets. This means that I have also given a treatment of Levy processes and their applications to ?nance, since these are central to most current thinking. Since this book was written the rigorous mathematical formulation of stochastic processes has developed considerably, most particularly towards greater precision and generality, and this has been re?ected in the way the subject is presented in m- ern applications, particularly in ?nance.

Recenzje

From the reviews of the fourth edition:

"This is the fourth edition of a textbook intended for everyone interested in practising stochastic 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)

Spis treści

A Historical Introduction.- Probability Concepts.- Markov Processes.- The Ito Calculus and Stochastic 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 Stochastic Differential Equations.

Blurb

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 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 approach to the white noise limit, on the applications of Poisson representation methods to population dynamics, and on several other applications of stochastic methods.

From the reviews of previous editions

"Extremely well written and informative... clear, complete, and fairly rigorous treatment of a larger number of very basic concepts in stochastic theory." (Journal of Quantum Electronics)

"A first class book." (Optica Acta)

"Ideal for people who need a clear introduction to stochastic mathematics and their applications in physical sciences… an excellent self study and reference book." (Quantnotes.com)

"This well-established volume takes a supreme position [among the many books on the subject].. This extremely valuable contribution to the field of applied stochastic methods can be recommended to graduate students, researchers, and university teachers." (Optimization)