论文标题
抛物面率的强烈收敛$ 1 $的随机allen-cahn型方程
Strong convergence of parabolic rate $1$ of discretisations of stochastic Allen-Cahn-type equations
论文作者
论文摘要
考虑随机allen-cahn型方程的近似值（即$ 1+1 $ 1 $ - 维度时空白噪声驱动的随机PDE，具有多项式非线性$ f $ $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f》（\ pm \ pm \ infty）= \ mp \ mp \ infty $）通过完全离散的空间时空expimic expime expimic expime expicit expimit expiente expicit exectiit exectition exectition exipe exitiite extice差异。严格的下限支持的文献共识是，相对于抛物线网格网格的强大收敛率$ 1/2 $预计将是最佳的。我们表明，通过暂时“假装” SPDE是单数的，可以在测量适当的负BESOV规范中测量误差时几乎确定收敛率$ 1 $（并且没有更好）。
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.
