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Convergence of an Operator Splitting Scheme for Abstract Stochastic Evolution Equations

Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 41)

Abstract

In this paper, we study the convergence of a Lie-Trotter operator splitting for stochastic semilinear evolution equations in a Hilbert space. The abstract Hilbert space setting allows for the consideration of convergence of the approximation for both the original and spatially discretized problems. It is known that the strong convergence of this scheme is classically of half-order, at best. We demonstrate that this is in fact the optimal order of convergence in the proposed setting, with the actual order being dependent upon the regularity of noise collected from applications.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA
  2. 2.Department of Mathematics and Center for Astrophysics, Space Physics and Engineering ResearchBaylor UniversityWacoUSA

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