Bregman variation of semimartingales

Prelegent(ci)

Dominik Kutek

Afiliacja

University of Warsaw

Język referatu

angielski

Termin

21 listopada 2024 12:15

Pokój

p. 3160

Tytuł w języku polskim

Bregman variation of semimartingales

Seminarium

Seminarium Zakładu Rachunku Prawdopodobieństwa

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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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