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|All Authors / Contributors:||
Mihael Perman; Wendelin Werner
|Responsibility:||Mihael Perman, Wendelin Werner.|
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).
- matematika -- verjetnostni račun -- stohastični procesi -- Brownovo gibanje -- krepka edinost -- teorija ekskurzij -- Ray-Knightovi izreki
- mathematics -- probability theory -- stochastic processes -- excursion theory -- local times -- Brownian motion -- Ray-Knight theorems -- strong uniqueness