The Bregman variation of semimartingales

20.11.2025, 13:00 Uhr  –  Haus 9, Raum 2.22
Forschungsseminar Diskrete Spektraltheorie

Katarzyna Pietruska-Paluba

We introduce a generalization of the quadratic variation of a (semi)martingale: the increments of a process will be measured with the so-called Bregman divergence (instead of the quadratic function). The Bregman variation process can be also defined through stochastic calculus. This process enjoys a Ito-type isometry formula, which allows for  applications in harmonic analysis. As examples, we prove Hardy-Stein identities for semigroups related to Levy processes, both in the elliptic and parabolic settings.