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 ε→0 of the process conditioned on remaining above −ε 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.

Type de document :
Article dans une revue
Progress in Probability, 2015, 69, pp.101-117. 〈10.1007/978-3-319-13984-5_5〉
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https://hal.archives-ouvertes.fr/hal-01392197
Contributeur : Okina Université d'Angers <>
Soumis le : vendredi 4 novembre 2016 - 10:46:16
Dernière modification le : lundi 5 février 2018 - 15:00:03

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Loïc Chaumont, Geronimo Uribe. Shifting Processes with Cyclically Exchangeable Increments at Random. Progress in Probability, 2015, 69, pp.101-117. 〈10.1007/978-3-319-13984-5_5〉. 〈hal-01392197〉

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