Invariance problems for stochastic partial differential equations

• Applicant: Dr. Stefan Tappe
• Subject Area: Mathematics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 444121509

Let a stochastic partial differential equation be given. In this project, we are interested to investigate when a set of the state space is invariant for this equation. This means that for every starting point from the set the corresponding solution of the stochastic partial differential equations stays in the set; in this case we speak about stochastic invariance. The essential goals of my project consist of a theoretical part and an application part. The general goal of the theoretical part is to solve problems concerning stochastic invariance; here the given set can be, for example, a convex cone, a submanifold, or an arbitrary closed subset of the state space. Afterwards, the general goal of the application part is to apply the previous findings of the theoretical part to stochastic partial differential equations from various fields; this covers equations arising in natural sciences, equations in financial and actuarial mathematics, and equations for modeling energy markets.

• DFG Programme: Research Grants