Abstract: We present several Itô-Wentzell formulae on Wiener spaces for real-valued functionals of random fields of Itô type depending on measures. We distinguish the full- and conditional-measure flow cases. Derivatives with respect to the measure components are understood in the sense of Lions.
We discuss additionally the Malliavin differentiability of McKean-Vlasov stochastic differential equations with common noise under the global Lipschitz assumption in the space variable and the measure variable. Our result gives meaning to the Malliavin derivative of the random probability measure that is the conditional law.
Ito-Wentzell-Lions formula and Malliavin calculus for (conditional) measure dependent random fields
10.04.2025 17:00 - 18:00
Location:
TU Wien, Wiedner Hauptstraße 8, 1040 Wien, "Freihaus" building, yellow section, 7th floor, seminar room DB gelb 07