Shifting Processes with Cyclically Exchangeable Increments at Random

International audience

<p>We propose a path transformation which applied to a cyclically exchangeable increment process conditions its minimum to belong to a given interval.</p><p>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.</p><p>We examine the consequences of this path transformation on processes with exchangeable increments, Lévy bridges, and the Brownian bridge.</p>