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Advances in Mathematical Methods and High Performance Computing pp 163–179Cite as

Convergence of an Operator Splitting Scheme for Abstract Stochastic Evolution Equations

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Part of the book series: Advances in Mechanics and Mathematics ((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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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, 79409-1042, USA

    Joshua L. Padgett

  2. Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, TX, 76798-7328, USA

    Qin Sheng

Authors
  1. Joshua L. Padgett
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  2. Qin Sheng
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Corresponding author

Correspondence to Joshua L. Padgett .

Editor information

Editors and Affiliations

  1. Department of Applied Science and Humanities, Inderprastha Engineering College, Ghaziabad, Uttar Pradesh, India

    Vinai K. Singh

  2. School of Science and Technology, Federation University Australia, Mt. Helen, VIC, Australia

    David Gao

  3. Institute of Numerical Mathematics, Technische Universität Dresden, Dresden, Germany

    Andreas Fischer

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Padgett, J.L., Sheng, Q. (2019). Convergence of an Operator Splitting Scheme for Abstract Stochastic Evolution Equations. In: Singh, V., Gao, D., Fischer, A. (eds) Advances in Mathematical Methods and High Performance Computing. Advances in Mechanics and Mathematics, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-030-02487-1_9

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