9783642393631
IR
EN-52312
انگلیسی
IR
Stochastic Simulation and Monte Carlo Method
[Book]
:Mathematical Foundations of Stochastic Simulation
/ by Carl Graham, Denis Talay
Berlin, Heidelberg
: Springer Berlin Heidelberg :Imprint: Springer,
, 2013.
XVI, 260 p. 4 illus., online resource.
(Stochastic Modelling and Applied Probability,0172-4568
; 68)
Electronic
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 differential equations. In particular, they review the essential properties of It?لإ integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.
Part I:Principles of Monte Carlo Methods -- 1.Introduction -- 2.Strong Law of Large Numbers and Monte Carlo Methods -- 3.Non Asymptotic Error Estimates for Monte Carlo Methods -- Part II:Exact and Approximate Simulation of Markov Processes -- 4.Poisson Processes -- 5.Discrete-Space Markov Processes -- 6.Continuous-Space Markov Processes with Jumps -- 7.Discretization of Stochastic Differential Equations -- Part III:Variance Reduction, Girsanov's Theorem, and Stochastic Algorithms -- 8.Variance Reduction and Stochastic Differential Equations -- 9.Stochastic Algorithms -- References -- Index.?╗╣
Stochastic Modelling and Applied Probability,0172-4568
68
Mathematics
Finance
Numerical analysis
Distribution (Probability theory)
Electronic books
E-BOOK
Graham, Carl.
Talay, Denis
SpringerLink (Online service)
ایران
9783642393624.pdf
عادی
عادی
9783642393624.pdf
متن
old catalog
e
BL
1
a
Y
