Stochastic Methods

This classic text and reference collects the many formulae and methods that can be found in the scientific literature on stochastic methods. This fourth edition has been thoroughly updated and restructured, and features a large amount of entirely new material.

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 )

The leading reference text in the field for many years and continuously updated and expanded. Features new sections and chapters on quantitative finance, adiabatic elimination and simulation methods. Rewritten in many places for better clarity and more in-depth mathematical exposition Includes supplementary material: sn.pub/extras

Inhalt
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.

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