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

该项目的目标是识别一个最近构建的无限维随机过程（与布朗桥的模量作为不变测度的法律）的解决方案，以SPDE反射以及识别作为随机热方程的解决方案的模量。此外，它的目的是证明粘性反射扭曲布朗运动序列的收敛到无穷维过程。为了识别它计划显示一个集成的部分公式相对于法律的布朗桥的模量的意义上的分布。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.