Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients

Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients
Author :
Publisher : American Mathematical Soc.
Total Pages : 112
Release :
ISBN-10 : 9781470409845
ISBN-13 : 1470409844
Rating : 4/5 (844 Downloads)

Book Synopsis Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients by : Martin Hutzenthaler

Download or read book Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients written by Martin Hutzenthaler and published by American Mathematical Soc.. This book was released on 2015-06-26 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, the authors establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method. These moment bounds are then used to prove strong convergence of the proposed schemes. Finally, the authors illustrate their results for several SDEs from finance, physics, biology and chemistry.


Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients Related Books

Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients
Language: en
Pages: 112
Authors: Martin Hutzenthaler
Categories: Mathematics
Type: BOOK - Published: 2015-06-26 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately
Monte Carlo and Quasi-Monte Carlo Methods
Language: en
Pages: 476
Authors: Art B. Owen
Categories: Computers
Type: BOOK - Published: 2018-07-03 - Publisher: Springer

DOWNLOAD EBOOK

This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that wa
Exact Finite-Difference Schemes
Language: en
Pages: 248
Authors: Sergey Lemeshevsky
Categories: Mathematics
Type: BOOK - Published: 2016-09-26 - Publisher: Walter de Gruyter GmbH & Co KG

DOWNLOAD EBOOK

Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact
Numerical Methods for Stochastic Partial Differential Equations with White Noise
Language: en
Pages: 391
Authors: Zhongqiang Zhang
Categories: Mathematics
Type: BOOK - Published: 2017-09-01 - Publisher: Springer

DOWNLOAD EBOOK

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begi
Taylor Approximations for Stochastic Partial Differential Equations
Language: en
Pages: 224
Authors: Arnulf Jentzen
Categories: Mathematics
Type: BOOK - Published: 2011-12-08 - Publisher: SIAM

DOWNLOAD EBOOK

This book presents a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations (SPDEs). The authors show how Taylor