5 papers · 1 filter
Small cover approach to the suprema of positive canonical processes
Witold Bednorz, RafaÅ Martynek, RafaÅ Meller
We extend the recent result of Park and Pham concerning the positive selector process to canonical processes generated by i.i.d. nonnegative random variables satisfying minimal tai…
The suprema of selector processes with the application to positive infinitely divisible processes
Witold Bednorz, RafaÅ Martynek, RafaÅ Meller
We provide an alternative proof of the recent result by Park and Pham (2022) on the expected suprema of positive selector and empirical processes. We extend it to positive infinite…
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…
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…
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…