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Domain preserving splitting schemes for a class of SPDEs driven by a standard Brownian motion

  • Charles-Édouard Bréhier
  • David Cohen
  • Gijs Custers
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Abstract

We consider a class of SPDEs driven by a standard real-valued Brownian motion, with drift and diffusion coefficients such that there exists a unique mild solution taking values in the interval [−1,1] almost surely. To preserve this qualitative property of the exact solution, we propose a domain preserving Lie--Trotter splitting scheme: for any choice of the time-step size, the numerical solution takes values in the interval [−1,1] almost surely. Furthermore, we prove mean-square convergence with rate 1/2− for the domain preserving Lie--Trotter scheme. These theoretical results are illustrated with numerical experiments.

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Cite

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BibTeX
@misc{brehier2026domain,
  title = {{Domain preserving splitting schemes for a class of SPDEs driven by a standard Brownian motion}},
  author = {Charles-Édouard Bréhier and David Cohen and Gijs Custers},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29950},
  eprint = {2609.29950},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05764532v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Domain preserving splitting schemes for a class of SPDEs driven by a standard Brownian motion
AU  - Charles-Édouard Bréhier
AU  - David Cohen
AU  - Gijs Custers
PY  - 2026
DA  - 2026/09/24
PB  - HAL
DO  - 10.48550/arxiv.2609.29950
UR  - https://hal.science/hal-05764532v1
AB  - We consider a class of SPDEs driven by a standard real-valued Brownian motion, with drift and diffusion coefficients such that there exists a unique mild solution taking values in the interval [−1,1] almost surely. To preserve this qualitative property of the exact solution, we propose a domain preserving Lie--Trotter splitting scheme: for any choice of the time-step size, the numerical solution takes values in the interval [−1,1] almost surely. Furthermore, we prove mean-square convergence with rate 1/2− for the domain preserving Lie--Trotter scheme. These theoretical results are illustrated with numerical experiments.
ER  -