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math.PR2025
Concentration of the truncated variation of fractional Brownian motions of any Hurst index, their -variations and local times
Witold M. Bednorz, Rafał M. Łochowski
We obtain bounds for probabilities of deviations of the truncated variation functional of fractional Brownian motions (fBm) of any Hurst index from their expected val…
math.PR2025
The It{ô}-Föllmer formula -- nonstandard cases
W. M. Bednorz, R. M. Łochowski, P. L. Zondi +2
The purpose of this note is to prove the It{ô}-Föllmer formula for the càdlàg paths possessing quadratic variation in a possibly ``weakest'' sense along some sequence of partitions…