Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Wang, Chengshi
Institution: Fudan University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221552362