Some points on Vervaat's transform of Brownian bridges and Brownian motion

Titus Lupu

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arXiv · 1308.3759

Some points on Vervaat's transform of Brownian bridges and Brownian motion

Titus Lupu

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Abstract

In a recent work J. Pitman and W. Tang defined the Vervaat's transform for a Brownian bridge with two different endpoints and for a Brownian motion between times $0$ and $1$. They proved some path decomposition properties for these Vervaat's transforms and raised open questions on their semi-martingale decomposition. In this paper we give an alternative proof for the path decomposition and answer the open questions.

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Titus Lupu. 2013-08-17. Some points on Vervaat's transform of Brownian bridges and Brownian motion. https://arxiv.org/abs/1308.3759

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