Journal article
The Galerkin analysis for the random periodic solution of semilinear stochastic evolution equations
- Abstract:
- In this paper, we study the numerical method for approximating the random periodic solution of semilinear stochastic evolution equations. The main challenge lies in proving a convergence over an infinite time horizon while simulating infinite-dimensional objects. We first show the existence and uniqueness of the random periodic solution to the equation as the limit of the pull-back flows of the equation, and observe that its mild form is well defined in the intersection of a family of decreasing Hilbert spaces. Then, we propose a Galerkin-type exponential integrator scheme and establish its convergence rate of the strong error to the mild solution, where the order of convergence directly depends on the space (among the family of Hilbert spaces) for the initial point to live. We finally conclude with a best order of convergence that is arbitrarily close to 0.5.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 447.0KB, Terms of use)
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- Publisher copy:
- 10.1007/s10959-023-01236-x
Authors
- Publisher:
- Springer
- Journal:
- Journal of Theoretical Probability More from this journal
- Volume:
- 37
- Issue:
- 1
- Pages:
- 133-159
- Publication date:
- 2023-01-25
- Acceptance date:
- 2023-01-05
- DOI:
- EISSN:
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1572-9230
- ISSN:
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0894-9840
- Language:
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English
- Keywords:
- Pubs id:
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1325382
- Local pid:
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pubs:1325382
- Deposit date:
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2023-01-26
Terms of use
- Copyright holder:
- Wu and Yuan
- Copyright date:
- 2023
- Rights statement:
- Copyright © 2023, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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