Developed from the author's course at the Ecole Polytechnique,
Monte-Carlo Methods and Stochastic Processes: From Linear to
Non-Linear focuses on the simulation of stochastic processes in
continuous time and their link with partial differential equations
(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. The book begins with a history of Monte-Carlo methods and
an overview of three typical Monte-Carlo problems: numerical
integration and computation of expectation, simulation of complex
distributions, and stochastic optimization. The remainder of the
text is organized in three parts of progressive difficulty. The
first part presents basic tools for stochastic simulation and
analysis of algorithm convergence. The second part describes
Monte-Carlo methods for the simulation of stochastic differential
equations. The final part discusses the simulation of non-linear
dynamics.
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