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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.

Produktbeschreibung
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.


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Autorenporträt
Emmanuel Gobet is a professor of applied mathematics at Ecole Polytechnique. His research interests include algorithms of probabilistic type and stochastic approximations, financial mathematics, Malliavin calculus and stochastic analysis, Monte Carlo simulations, statistics for stochastic processes, and statistical learning.