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Article Dans Une Revue Electronic Journal of Probability Année : 2022

Rate of escape of conditioned Brownian motion

Résumé

We study the norm of the two-dimensional Brownian motion conditioned to stay outside the unit disk at all times. We obtain sharp results on the rate of escape to infinity of the process of future minima. For this, we introduce a renewal structure attached to record times and values. Additional results are given for the long time behavior of the norm.
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Dates et versions

hal-03146283 , version 1 (18-02-2021)
hal-03146283 , version 2 (04-04-2021)
hal-03146283 , version 3 (27-10-2021)

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Citer

Orphée Collin, Francis Comets. Rate of escape of conditioned Brownian motion. Electronic Journal of Probability, 2022, 27, ⟨10.1214/21-ejp737⟩. ⟨hal-03146283v3⟩
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