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arXiv · 2610.13561

An infinite-dimensional representation of Ray-Knight theorems for the Bass-Burdzy flow

Chengshi Wang
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Abstract

[Bass and Burdzy 1999] introduced a stochastic flow of homeomorphisms of the real line $\mathcal R_t:x\mapsto \mathcal R_t(x)$, driven by a Brownian motion. Ray-Knight theorems for the process $\mathcal R_t^{-1}(0)$ were later obtained by [Hu and Warren 2000]. We extend their results by proving an integral representation driven by a common white noise for the local times of $\mathcal R_t^{-1}(0)$, in analogy with the case of the standard Ray-Knight theorems [Aïdékon, Hu and Shi 2024]. We generalize this representation to the setting of a Bass-Burdzy flow driven by a drifted Brownian motion perturbed at its maximum, and use this framework to answer a question of [Aïdékon, Hu and Shi 2026] concerning the description of the conditional law of a perturbed reflecting Brownian motion given its occupation measure in terms of Bass-Burdzy flows.

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Chengshi Wang. 2026-10-09. An infinite-dimensional representation of Ray-Knight theorems for the Bass-Burdzy flow. https://arxiv.org/abs/2610.13561

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