Dear Colleagues,

We would like to invite you to the following SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi:

Semimartingales with jumps, weak Dirichlet processes and path-dependent martingale problems
by Francesco Russo (ENSTA-Paris)

The seminar will take place on TUE, 23.05.2023 at 14:00 CET in Aula Seminari, Department of Mathematics, University of Pisa and streamed online here.

The organizers,
A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco
https://sites.google.com/unipi.it/spass

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Abstract: In this talk we will revisit the notion of weak Dirichlet process which is the natural extension of semimartingale with jumps. If X is such a process, then it is the sum of a local martingale M and a martingale ortogonal process A in the sense that [A, N] = 0 for every continuous local martingale N . We remark that if [A] = 0 then X is a Dirichlet process. The notion of Dirichlet process is not very suitable in the jump case since in this case A is forced to be continuous.
The talk will discuss the following points.
1. To provide a (unique) decomposition which is also new for semimartingales with jumps.
2. To discuss some new stability theorem for weak Dirichlet processes through C^{0,1} transformations.
3. To discuss various examples of such processes arising from path-dependent martingale problems. This includes path-dependent stochastic differential equations involving a distributional drift and with jumps.
The talk is based on a joint paper with E. Bandini (Bologna).