Wednesday, August 2, 2023 - 14:00 in V3-201 + Zoom
Semimartingales with jumps, weak Dirichlet processes and path-dependent martingale problems
A talk in the Bielefeld Stochastic Afternoon series by
Francesco Russo
| 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.
(i) To provide a (unique) decomposition which
is also new for semimartingales with jumps.
(ii) To discuss some new stability theorem
for weak Dirichlet processes through $C^{0,1}$
transformations.
(iii) To discuss various examples of such processes
arising from path-dependent martingale problems.
This includes path-dependent stochastic differential equations
with involving a distributional drift and with jumps.
The talk is based on a joint paper with E. Bandini (Bologna).
Within the CRC this talk is associated to the project(s): B1 |
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