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Shifting processes with cyclically exchangeable increments at random

Abstract : We propose a path transformation which applied to a cyclically exchangeable increment process conditions its minimum to belong to a given interval. This path transformation is then applied to processes with start and end at 0. It is seen that, under simple conditions, the weak limit as $\varepsilon\rightarrow0$ of the process conditioned on remaining above $-\varepsilon$ exists and has the law of the Vervaat transformation of the process. We examine the consequences of this path transformation on processes with exchangeable increments, Lévy bridges, and the Brownian bridge.
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Contributor : Loïc Chaumont <>
Submitted on : Friday, July 11, 2014 - 2:45:41 PM
Last modification on : Monday, March 9, 2020 - 6:15:54 PM
Long-term archiving on: : Saturday, October 11, 2014 - 12:45:29 PM


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  • HAL Id : hal-01023079, version 1



Loïc Chaumont, Gerónimo Uribe Bravo. Shifting processes with cyclically exchangeable increments at random. 2014. ⟨hal-01023079⟩



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