An infinite-dimensional representation of Ray-Knight theorems for the Bass-Burdzy flow
Abstract
[Bass and Burdzy 1999] introduced a stochastic flow of homeomorphisms of the real line ℛt:x↦ ℛt(x), driven by a Brownian motion. Ray-Knight theorems for the process ℛt−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 ℛt−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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BibTeX
@misc{wang2026infinitedimensional,
title = {{An infinite-dimensional representation of Ray-Knight theorems for the Bass-Burdzy flow}},
author = {Chengshi Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13561},
eprint = {2610.13561},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13561},
}
RIS
TY - UNPB
TI - An infinite-dimensional representation of Ray-Knight theorems for the Bass-Burdzy flow
AU - Chengshi Wang
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13561
UR - https://arxiv.org/abs/2610.13561
AB - [Bass and Burdzy 1999] introduced a stochastic flow of homeomorphisms of the real line ℛ_t:x↦ ℛ_t(x), driven by a Brownian motion. Ray-Knight theorems for the process 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 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.
ER -