Analysis and approximation of infinite dimensional sticky reflected Ornstein-Uhlenbeck processes

该项目的目标是确定一个最近构造的无限维随机过程（以布朗桥的模量定律作为不变测度）作为具有反射的SPDE的解，以及作为随机热方程解的模量的识别。此外，它旨在证明粘反射变形布朗运动序列对无限维过程的收敛性。为了证明这一点，计划在分布的意义上给出一个关于布朗桥的模量定律的分部积分公式。为了推导过程的收敛性，目的是证明相应的狄利克雷形式的Mosco收敛性。另一个目标是证明非高斯极限-狄利克雷形式的Log-Sobolev不等式。最后，我们计划将这些概念推广到保守模型和更高的维度。

The goal of the project is the identification of a recently constructed infinite dimensional stochastic process (with the law of the modulus of the Brownian bridge as invariant measure) as the solution to an SPDE with reflection as well as the identification as the modulus of the solution of the stochastic heat equation. Moreover, it is intended to prove convergence of a sequence of sticky reflected distorted Brownian motions to the infinite dimensional process. For the identification it is planned to show an integration by parts formula with respect to the law of the modulus of the Brownian bridge in the sense of distributions. In order to deduce the convergence of processes the aim is to show Mosco convergence of the corresponding Dirichlet forms. An additional goal is to prove a Log-Sobolev inequality for the non-Gaussian Limit-Dirichlet form. Finally, we plan to generalize the concepts to the conservative model and higher dimensions.