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Perturbed Brownian motions
- "We study "perturbed Brownian motions", that can be, loosely speaking, describes as follows: they behave exactly as linear Brownian motion except they hit their maximum or minimum where they get an extra "push". We define with no restrictions on the perturbation parameters a process which has this property and show that its law is unique within a certain "natural class" of processes. In the case where both perturbations (at the maximum and at the minimum) are self-repelling, we show that in fact, moer is true: Such a process can almost surely be constructed from Brownian paths by a one-to-one measurable transformation. This generalizes some results of Carmona-Petit-Yor and Davis. We also derive some fine properties of perturbed Brownian motions (Hausdorff dimension of points of monotonicity for example)."
- "Članek obravnava stohastični proces, ki ga dobimo, če standardno Brownovo gibanje perturbiramo, ko doseže maksimum ali minimum, in sicer tako, da v tistem trenutku dodamo dušenje, ki Brownovo gibanje ali potiska od izhodišča ali proti izhodišču. Najprej je dokazana eksistenca takega procesa, potem pa so obravnavane njegove lastnosti. Nazadnje obravnavamo še lastnosti trajektorij perturbiranega Brownovega gibanja npr. Hausdorffova dimenzija točk mnogoterosti."
- "Perturbed Brownian motions"