Monte-Carlo Methods and Stochastic Processes

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

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.

Inhaltsverzeichnis

Introduction: brief overview of Monte-Carlo methods. TOOLBOX FOR STOCHASTIC SIMULATION: Generating random variables. Convergences and error estimates. Variance reduction. SIMULATION OF LINEAR PROCESS: Stochastic differential equations and Feynman-Kac formulas. Euler scheme for stochastic differential equations. Statistical error in the simulation of stochastic differential equations. SIMULATION OF NONLINEAR PROCESS: Backward stochastic differential equations. Simulation by empirical regression. Interacting particles and non-linear equations in the McKean sense. Appendix. Index.

Details

Erscheinungsjahr:	2020
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	Einband - flex.(Paperback)
ISBN-13:	9780367658465
ISBN-10:	0367658461
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Gobet, Emmanuel
Hersteller:	Taylor & Francis Chapman and Hall/CRC
Verantwortliche Person für die EU:	preigu GmbH & Co. KG, Lengericher Landstr. 19, D-49078 Osnabrück, mail@preigu.de
Maße:	18 x 156 x 234 mm
Von/Mit:	Emmanuel Gobet
Erscheinungsdatum:	30.09.2020
Gewicht:	0,485 kg