[AN] Gergely Bodo: Weak Lp inequalities for stochastic integrals

05 March 2024 16:00 till 17:00 - Location: Drebbelweg Instruction Room 4 | Add to my calendar

It is a well-known result of Rosiński and Woyczyński (1986) that for any α ∈ (0, 2), real-valued symmetric α-stable Lévy process L and real-valued predictable process Ψ one has

\(\sup_{r>0}r^\alpha\,P\left(\sup_{t \in [0,T]}\bigl\|\int_0^t \Psi \,{\rm d}L\bigr\|>r\right)\eqsim E\left[\int_0^T \vert \Psi(t) \vert^\alpha\, {\rm d}t\right].\)

The primary aim of this talk is to extend this result in two directions. First, it is possible to move away from the real-valued setting and consider stochastic integrals with operator-valued integrands with respect to cylindrical Lévy processes in Banach space. Second, instead of integrating with respect to a Lévy process, one might consider stochastic integrals with respect to general random measures.

This talk is based on an ongoing project with Ivan Yaroslavtsev.