Stochastic Methods

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.