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 Limited.- Beyond the White Noise Limit.- Levy Processes and Financial Applications.- Master Equations and Jump Processes.- The Poisson Representation.- Spatially Distributed Systems.- Bistability, Mestability, and Escape Problems.- Simulation of Stochastic Differential Equations.- References.- Bibliography.- Author Index.- Symbol Index.- Subject Index.
(source: Nielsen Book Data)
This classic text and reference collects, in simple language and deductive form, the many formulae and methods that can be found in the scientific literature on stochastic methods. To be useful to students and practitioners as a practical tool, the book is written without excessive mathematical rigour, yet restricted to those methods and approximations thereof, that can be systematized and controlled in a quantitative way. Over time, new editions have been expanded in scope for a widening readership that now encompasses all of the quantitative natural and social sciences. This fourth edition has been thoroughly updated and restructured, and features a large amount of entirely new material, including but not limited to aspects of driven stochastic systems, the application and validity of simulation methods as well as applications to financial markets. (source: Nielsen Book Data)