1. A Historical Introduction.
2. Probability Concepts.
3. Markov Processes.
4. The Ito Calculus and Stochastic Differential Equations.
5. The Fokker Planck Equation.
6. The Fokker Planck Equation in Several Dimensions.
7. Small Noise Approximations for Diffusion Processes.
8. The White Noise Limited.
9. Beyond the White Noise Limit.
10. Levy Processes and Financial Applications.
11. Master Equations and Jump Processes.
12. The Poisson Representation.
13. Spatially Distributed Systems.
14. Bistability, Mestability, and Escape Problems.
15. Simulation of Stochastic Differential Equations

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. --- summary provided by publisher