Orateur
Laurent Decreusefond
(LTCI, Télécom Paris)
Description
Joint work with L. Coutin
Solving the SDE $dX(t)=r(X(t)) dt + dB(t) (1)$ is equivalent invert the map $B\mapsto B(t)-\int_0^t r(B(s)) ds$.
We study the analog of this problem on the Poisson space. Because of the Girsanov Theorem, it turns out that equivalent problem consists in inverting a time change.
We can then reinterpret the solution of the generalized Hawkes problem (find a self excited point process for a given compensator) as the analog to solving an SDE like (1). We then show a Yamada-Watanabe like theorem for weak and strong solutions to the Hawkes problem.
Some relationships are also established between Hawkes processes and directed transport between point processes.
Auteur principal
Laurent Decreusefond
(LTCI, Télécom Paris)
