Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
Author(s)
Bibliographic Information
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
（Memoirs of the American Mathematical Society, no. 1112）
American Mathematical Society, 2015, c2014
Available at 8 libraries
Note
"Volume 236, number 1112 (second of 6 numbers), July 2015"
Includes bibliographical references (p. 95-99)
Description and Table of Contents
Description
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.
Table of Contents
Introduction
Integrability properties of approximation processes for SDEs
Convergence properties of approximation processes for SDEs
Examples of SDEs
Bibliography
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