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Shifting Processes with Cyclically Exchangeable Increments at Random

  • Loïc Chaumont
  • Gerónimo Uribe Bravo
Conference paper
Part of the Progress in Probability book series (PRPR, volume 69)

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 \(\varepsilon \rightarrow 0\) 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.

Keywords

Cyclic exchangeability Vervaat transformation Brownian bridge Three dimensional Bessel bridge Uniform law Path transformation Occupation time 

Mathematics Subject Classification (2010).

60G09 60F17 60G17 60J65 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LAREMA, Département de MathématiquesUniversité d’Angers, 2Angers Cedex 01France
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de México, Área de la Investigación Científica, Ciudad UniversitariaCiudad de MéxicoMéxico

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