Stochastic Processes

Pierre Del Moral and Spiridon Penev are professors in the School of Mathematics and Statistics at the University of New South Wales.

• An illustrated guide. Motivating examples. Selected topics. Computational & theoretical aspects. Stochastic simulation. Simulation toolbox. Monte Carlo integration. Some illustrations. Discrete time processes. Markov chains. Analysis toolbox. Computational toolbox. Continuous time processes. Poisson processes. Markov chain embeddings. Jump processes. Piecewise deterministic processes. Diffusion processes. Jump diffusion processes. Nonlinear jump diffusion processes. Stochastic analysis toolbox. Path space measures. Processes on manifolds. Stochastic differential calculus on manifolds. Parameterizations and charts. Stochastic calculus in chart spaces. Some analytical aspects. Some illustrations. Some application areas. Simple random walks. Iterated random functions. Computational & Statistical physics. Dynamic population models. Gambling, ranking and control. Mathematical finance.

"The title itself suggests that the reader should expect something different, applications to theory and not theory to applications. The title is correct, and that is the main theme of the book. Start with some general applications, and then build the theory around them. The range of applications and the depth of the discussions are impressive." (Igor Cialenco, Illinois Institute of Technology)"This is a great reference… It lays out a lot of calculations in simple and direct ways. If you go through this book as a first-year grad student, you will understand lots of material and be prepared for many things." (Richard Sowers, University of Illinois at Urbana-Champaign)"(This book makes) theoretical tools developed in the stochastic analysis/probability community available to a significant community of applied mathematicians. As such, it should be highly successful, as it is well written and clear." (John Fricks, The Pennsylvania State University)