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math.PR2023
Local times of deterministic paths and self-similar processes with stationary increments as normalized numbers of interval crossings
Witold Bednorz, Purba Das, Rafał Łochowski
We prove a general result on a relationship between a limit of normalized numbers of interval crossings by a càdlàg path and an occupation measure associated with this path. Using…
math.PR2023
Level crossings of fractional Brownian motion
Purba Das, Rafał Łochowski, Toyomu Matsuda +1
Since the classical work of Lévy, it is known that the local time of Brownian motion can be characterized through the limit of level crossings. While subsequent extensions of this…