Discrete stochastic maximal regularity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915679946407936 |
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| author | Evangelopoulos-Ntemiris, Foivos Veraar, Mark |
| author_facet | Evangelopoulos-Ntemiris, Foivos Veraar, Mark |
| contents | In this paper, we investigate discrete regularity estimates for a broad class of temporal numerical schemes for parabolic stochastic evolution equations. We provide a characterization of discrete stochastic maximal $\ell^p$-regularity in terms of its continuous counterpart, thereby establishing a unified framework that yields numerous new discrete regularity results. Moreover, as a consequence of the continuous-time theory, we establish several important properties of discrete stochastic maximal regularity such as extrapolation in the exponent $p$ and with respect to a power weight. Furthermore, employing the $H^\infty$-functional calculus, we derive a powerful discrete maximal estimate in the trace space norm $D_A(1-\frac1p,p)$ for $p \in [2,\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete stochastic maximal regularity Evangelopoulos-Ntemiris, Foivos Veraar, Mark Analysis of PDEs Numerical Analysis Functional Analysis Probability Primary: 46N40, 60H15, Secondary: 35B65, 42B37, 47D06, 60H35, 65J10, 65M12 In this paper, we investigate discrete regularity estimates for a broad class of temporal numerical schemes for parabolic stochastic evolution equations. We provide a characterization of discrete stochastic maximal $\ell^p$-regularity in terms of its continuous counterpart, thereby establishing a unified framework that yields numerous new discrete regularity results. Moreover, as a consequence of the continuous-time theory, we establish several important properties of discrete stochastic maximal regularity such as extrapolation in the exponent $p$ and with respect to a power weight. Furthermore, employing the $H^\infty$-functional calculus, we derive a powerful discrete maximal estimate in the trace space norm $D_A(1-\frac1p,p)$ for $p \in [2,\infty)$. |
| title | Discrete stochastic maximal regularity |
| topic | Analysis of PDEs Numerical Analysis Functional Analysis Probability Primary: 46N40, 60H15, Secondary: 35B65, 42B37, 47D06, 60H35, 65J10, 65M12 |
| url | https://arxiv.org/abs/2505.22145 |