论文标题
二维圆环上缓慢依赖时间依赖的单数SPDE的浓度估计值
Concentration estimates for slowly time-dependent singular SPDEs on the two-dimensional torus
论文作者
论文摘要
我们考虑在二维圆环上缓慢依赖时间依赖性的奇异随机偏微分方程，该方程是由弱时空白噪声驱动的，并且在灯芯上重新拟合。我们的主要结果是浓度在方程稳定平衡分支附近的样品路径上，没有噪声，在适当的BESOV和Hölder规范中测量。我们还讨论了一个涉及干草叉分叉的案件。这些结果扩展到[Berglund和Gentz，Pro-and Gentz，2002]中获得的二维圆环，用于有限维的SDE，以及[Berglund and Nader，Stochastics and PDES，2022]中的SPDES的SPDES。
We consider slowly time-dependent singular stochastic partial differential equations on the two-dimensional torus, driven by weak space-time white noise, and renormalised in the Wick sense. Our main results are concentration results on sample paths near stable equilibrium branches of the equation without noise, measured in appropriate Besov and Hölder norms. We also discuss a case involving a pitchfork bifurcation. These results extend to the two-dimensional torus those obtained in [Berglund and Gentz, Proability Theory and Related Fields, 2002] for finite-dimensional SDEs, and in [Berglund and Nader, Stochastics and PDEs, 2022] for SPDEs on the one-dimensional torus.
