Bregman variation of semimartingales

Speaker(s)

Dominik Kutek

Affiliation

University of Warsaw

Language of the talk

English

Date

Nov. 21, 2024, 12:15 p.m.

Room

room 3160

Title in Polish

Bregman variation of semimartingales

Seminar

Seminar of Probability Group

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The quadratic variation is a key concept in stochastic calculus, with widespread applications in mathematics and economy. The talk will be about a similar, but more general concept, the Bregman variation (or phi-variation) of semimartingales. In analogy to the quadratic case, we will study pathwise representation and Itô-type isometry for Bregman variation. As shall be seen, this concept is tailor-made for studying phi-integrable semimartingales and problems of probability and analysis that involve convex functions more general than the quadratic function. We give applications to semigroups, harmonic analysis and martingales. In particular, we will discuss Hardy-Stein identities in L_phi(R^d) for semigroups of Lévy processes satisfying certain mild assumptions.

Based on a joint work with Krzysztof Bogdan and Katarzyna Pietruska-Pałuba.

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