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.
