Krzysztof Bogdan

collaborators

2 papers

math.CA2025

Polarized Hardy--Stein identity

Krzysztof Bogdan, MichaÅ Gutowski, Katarzyna Pietruska-PaÅuba

We prove the Hardy--Stein identity for vector functions in $L^{p} (R^{d}; R^{n})$ with $1 < p < \infty$ and for the canonical paring of two real functions in $L^{p} (R^{d})$ …

math.PR2024

Bregman variation of semimartingales

Krzysztof Bogdan, Dominik Kutek, Katarzyna Pietruska-PaÅuba

We define Bregman variation of semimartingales. We give its pathwise representation, ItÃ´-type isometry for martingales, and applications to harmonic analysis.