Strong convergence of parabolic rate $1$ of discretisations of stochastic Allen-Cahn-type equations
| Autor: | Gerencsér, Máté, Singh, Harprit |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Trans. Amer. Math. Soc. 377 (2024), 1851-1881 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/tran/9029 |
| Popis: | Consider the approximation of stochastic Allen-Cahn-type equations (i.e. $1+1$-dimensional space-time white noise-driven stochastic PDEs with polynomial nonlinearities $F$ such that $F(\pm \infty)=\mp \infty$) by a fully discrete space-time explicit finite difference scheme. The consensus in literature, supported by rigorous lower bounds, is that strong convergence rate $1/2$ with respect to the parabolic grid meshsize is expected to be optimal. We show that one can reach almost sure convergence rate $1$ (and no better) when measuring the error in appropriate negative Besov norms, by temporarily `pretending' that the SPDE is singular. Comment: 34 pages, 3 figures |
| Databáze: | arXiv |
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