Stochastic Analysis and SDEs

We are interested in Stochastic Differential Equations of various types and related questions from real and harmonic analysis. Here we apply analytical methods to treat the probabilistic problems. For example, we analyse regularity properties of backwards stochastic differential equations, stochastic integrals, and stochastic processes using methods from interpolation theory, PDE theory, harmonic analysis, and function spaces. And we go the other way around as we treat regularity properties of partial differential integral equations (PDIEs) using probabilistic tools.

Research interests

• Malliavin calculus and Besov spaces.
• Stochastic differential equations of various types and their 
  regularity and approximation, especially backward equations, 
  McKean-Vlasov equation, equations driven by jump processes.
• Non-linear PDEs and BSDEs.
• Regularity and interpolation theory for SDEs.