Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations
Abstract
Exponential integrability properties of numerical approximations are a key tool for establishing positive rates of strong and numerically weak convergence for a large class of nonlinear stochastic differential equations. It turns out that wellknown numerical approximation processes such as EulerMaruyama approximations, linearimplicit Euler approximations, and some tamed Euler approximations from the literature rarely preserve exponential integrability properties of the exact solution. The main contribution of this article is to identify a class of stopped incrementtamed Euler approximations which preserve exponential integrability properties of the exact solution under minor additional assumptions on the involved functions.
 Publication:

arXiv eprints
 Pub Date:
 September 2013
 arXiv:
 arXiv:1309.7657
 Bibcode:
 2013arXiv1309.7657H
 Keywords:

 Mathematics  Numerical Analysis;
 Mathematics  Probability;
 65C30
 EPrint:
 39 pages