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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, RafaÅ M. Åochowski
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. Åochowski, P. L. Zondi +2
The purpose of this note is to prove the It{ô}-Föllmer formula for the cà dlà g paths possessing quadratic variation in a possibly ``weakest'' sense along some sequence of partit…
math.PR2024
Local times of deterministic paths and self-similar processes with stationary increments as normalized numbers of interval crossings
Witold Bednorz, Purba Das, RafaÅ Åochowski
We prove a general result on a relationship between a limit of normalized numbers of interval crossings by a cà dlà g path and an occupation measure associated with this path. Usin…