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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 approximation 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 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 stochastic 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 stochastic 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.
List of contents
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.
Summary
The Handbook of Stochastic Methods covers systematically and in simple language the foundations of Markov systems, stochastic differential equations, Fokker-Planck equations and stochastic master equations. Strong emphasis is placed on systematic approximation methods for solving problems. The practical orientation and broad coverage will appeal to researchers and academics working in theoretical physics, physical chemistry and mathematical finance.
The inclusion of a new chapter on the numerical treatment of stochastic differential equations further enhances the value of the third edition of this classic text for practitioners.
From the reviews: "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)
Additional text
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)
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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)
