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

• Applicant: Professor Dr. Martin Grothaus
• Subject Area: Mathematics
• Term: from 2016 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 324039129

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.

• DFG Programme: Research Grants