عنوان

Stochastic Simulation and Monte Carlo Method

(Number (ISBN

9783642393631

Country Code

IR

Number

EN-52312

.Language of Text, Soundtrack etc

انگلیسی

Country of publication

IR

Title Proper

Stochastic Simulation and Monte Carlo Method

General Material Designation

[Book]

Other Title Information

:Mathematical Foundations of Stochastic Simulation

First Statement of Responsibility

/ by Carl Graham, Denis Talay

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

: Springer Berlin Heidelberg :Imprint: Springer,

Date of Publication, Distribution, etc.

, 2013.

Specific Material Designation and Extent of Item

XVI, 260 p. 4 illus., online resource.

Series Title

(Stochastic Modelling and Applied Probability,0172-4568

Volume Designation

; 68)

Text of Note

Electronic

Text of Note

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.

Text of Note

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.?╗╣

Title

Stochastic Modelling and Applied Probability,0172-4568

Volume Number

68

Mathematics

Finance

Numerical analysis

Distribution (Probability theory)

Electronic books

Class number

Graham, Carl.

Talay, Denis

SpringerLink (Online service)

Country

ایران

Host name

9783642393624.pdf

Access number

عادی

Compression information

عادی

Date and Hour of Consultation and Access

9783642393624.pdf

Electronic Format Type

متن

old catalog

e

BL

1

a

Y