Quantifying the effect of graph structure on strong Feller property of SPDEs
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910019957555200 |
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| author | Cui, Jianbo Dang, Tonghe Hong, Jialin Wang, Zhengkai |
| author_facet | Cui, Jianbo Dang, Tonghe Hong, Jialin Wang, Zhengkai |
| contents | This paper investigates how the structure of the underlying graph influences the behavior of stochastic partial differential equations (SPDEs) on finite tree graphs, where each edge is driven by space-time white noise. We first introduce a novel graph-based null decomposition approach to analyzing the strong Feller property of the Markov semigroup generated by SPDEs on tree graphs. By examining the positions of zero entries in eigenfunctions of the graph Laplacian operator, we establish a sharp upper bound on the number of noise-free edges that ensures both the strong Feller property and irreducibility. Interestingly, we find that the addition of noise to any single edge is sufficient for chain graphs, whereas for star graphs, at most one edge can remain noise-free without compromising the system's properties. Furthermore, under a dissipative condition, we prove the existence and exponential ergodicity of a unique invariant measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11484 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantifying the effect of graph structure on strong Feller property of SPDEs Cui, Jianbo Dang, Tonghe Hong, Jialin Wang, Zhengkai Probability Numerical Analysis Analysis of PDEs 60H15, 35R02, 47D07, 37L40 This paper investigates how the structure of the underlying graph influences the behavior of stochastic partial differential equations (SPDEs) on finite tree graphs, where each edge is driven by space-time white noise. We first introduce a novel graph-based null decomposition approach to analyzing the strong Feller property of the Markov semigroup generated by SPDEs on tree graphs. By examining the positions of zero entries in eigenfunctions of the graph Laplacian operator, we establish a sharp upper bound on the number of noise-free edges that ensures both the strong Feller property and irreducibility. Interestingly, we find that the addition of noise to any single edge is sufficient for chain graphs, whereas for star graphs, at most one edge can remain noise-free without compromising the system's properties. Furthermore, under a dissipative condition, we prove the existence and exponential ergodicity of a unique invariant measure. |
| title | Quantifying the effect of graph structure on strong Feller property of SPDEs |
| topic | Probability Numerical Analysis Analysis of PDEs 60H15, 35R02, 47D07, 37L40 |
| url | https://arxiv.org/abs/2602.11484 |