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• W2024329804 abstract "We study `perturbed Brownian motions', that can be, loosely speaking, described as follows: they behave exactly as linear Brownian motion except when they hit their past maximum or/and maximum 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, more 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)." @default.
• W2024329804 created "2016-06-24" @default.
• W2024329804 creator A5066390619 @default.
• W2024329804 creator A5074326719 @default.
• W2024329804 date "1997-07-01" @default.
• W2024329804 modified "2023-10-18" @default.
• W2024329804 title "Perturbed Brownian motions" @default.
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• W2024329804 doi "https://doi.org/10.1007/s004400050113" @default.
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