Shifting Processes with Cyclically Exchangeable Increments at Random - Archive ouverte HAL Access content directly
Journal Articles Progress in Probability Year : 2015

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.

Dates and versions

hal-01392197 , version 1 (04-11-2016)

Identifiers

Cite

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⟩
88 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More