Title: Real Interpolation and Stochastic Differential Equations
Abstract: Using the real interpolation method from functional analysis one defines
the two-parametric scale of Malliavin Besov spaces on the Wiener space. The knowledge of the Besov regularity of a random variable on the Wiener space turned out to be crucial to understand certain phenomena.
In the talk I investigate the Besov regularity of solutions to path-dependent Stochastic Differential Equations (SDEs). As the real interpolation method is by its very definition a linear method,
but finding solutions to SDEs is a non-linear problem, the linear approach using the K- or J-method cannot be used. Instead, we use a coupling method, which gives raise to a general class of Besov spaces, that has been introduced in [1]. As an end-point case we obtain the Malliavin differentiability of SDEs under very general assumptions.
The talk is based on joint work with Xilin Zhou [2].
[1] S. Geiss and J.Ylinen:
Decoupling on the Wiener space, related Besov spaces, and
applications to BSDEs, Memoirs AMS 1335, 2021.
[2] S. Geiss and X. Zhou: Coupling of stochastic differential
equations on the Wiener space. arXiv:2412.10836.
Note that the starting time is 9.00am sharp.
