Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations

Hutzenthaler, Martin; Jentzen, Arnulf; Wang, Xiaojie

doi:10.1090/mcom/3146

Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations
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by Martin Hutzenthaler, Arnulf Jentzen and Xiaojie Wang;

Math. Comp. 87 (2018), 1353-1413

DOI: https://doi.org/10.1090/mcom/3146

Published electronically: March 31, 2017

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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 well-known numerical approximation processes such as Euler-Maruyama approximations, linear-implicit 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 increment-tamed Euler approximations which preserve exponential integrability properties of the exact solution under minor additional assumptions on the involved functions.

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