Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations

Authors

Martin Hutzenthaler, Arnulf Jentzen, and Diyora Salimova

Reference

Communications in Mathematical Sciences, Vol. 16, No. 6, pp. 1489-1529, 2018.

DOI: 10.4310/CMS.2018.v16.n6.a2

Abstract

This article introduces and analyzes a new explicit, easily implementable, and full-discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations (SPDEs) with possibly non-globally monotone nonlinearities such as stochastic Kuramoto–Sivashinsky equations. The main result of this article proves that the proposed approximation scheme converges strongly and numerically weakly to the solution process of such an SPDE. Key ingredients in the proof of our convergence result are a suitable generalized coercivity-type condition, the specific design of the accelerated exponential Euler-type approximation scheme, and an application of Fernique’s theorem.

Keywords

stochastic differential equation, strong convergence, numerical approximation, stochastic Kuramoto–Sivashinsky equations, coercivity-type condition, accelerated exponential Euler approximations

Download this document:

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.