Stochastic Simulation and Monte Carlo Methods : Mathematical Foundations of Stochastic Simulation

種類:

電子ブック

責任表示:

by Carl Graham, Denis Talay

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013

著者名:

• Graham, Carl
• Talay, Denis
• SpringerLink (Online service)

シリーズ名:

Stochastic Modelling and Applied Probability ; 68

ISBN:

9783642393631 [3642393632]    

注記:

In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic di

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