Monte-Carlo Methods and Stochastic Processes

This text focuses on the simulation of stochastic processes in continuous time and their link with PDEs. It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method. It presents basic tools for stochastic simulation and analysis of algorithm convergence, describes Monte-Carlo methods for the simulation of stochastic differential equations, and discusses the simulation of non-linear dynamics.