Stability analysis of a branching diffusion solver for semilinear heat equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908872511324160 |
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| author | Huang, Qiao Privault, Nicolas |
| author_facet | Huang, Qiao Privault, Nicolas |
| contents | Stochastic branching algorithms provide a useful alternative to grid-based schemes for the numerical solution of partial differential equations, particularly in high-dimensional settings. However, they require a strict control of the integrability of random functionals of branching processes in order to ensure the non-explosion of solutions. In this paper, we study the stability of a functional branching representation of PDE solutions by deriving sufficient criteria for the integrability of the multiplicative weighted progeny of stochastic branching processes. We also prove the uniqueness of mild solutions under uniform integrability assumptions on random functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability analysis of a branching diffusion solver for semilinear heat equations Huang, Qiao Privault, Nicolas Probability Analysis of PDEs 35K55, 35K58, 60H30, 60J85, 65C05 Stochastic branching algorithms provide a useful alternative to grid-based schemes for the numerical solution of partial differential equations, particularly in high-dimensional settings. However, they require a strict control of the integrability of random functionals of branching processes in order to ensure the non-explosion of solutions. In this paper, we study the stability of a functional branching representation of PDE solutions by deriving sufficient criteria for the integrability of the multiplicative weighted progeny of stochastic branching processes. We also prove the uniqueness of mild solutions under uniform integrability assumptions on random functionals. |
| title | Stability analysis of a branching diffusion solver for semilinear heat equations |
| topic | Probability Analysis of PDEs 35K55, 35K58, 60H30, 60J85, 65C05 |
| url | https://arxiv.org/abs/2502.17853 |