PreprintCC BY 4.0arXiv
From skew to reflected SPDEs
Abstract
In this article, we prove that the solution of the skew stochastic heat equation converges to the solution of the stochastic heat equation with reflection in the limit of infinite skewness. The result holds at equilibrium. This provides an SPDE analog of the link between skew and reflected Brownian motion. One of the intermediate results is the convergence in law of a penalised Brownian bridge to a 3-Bessel bridge.
Related
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BibTeX
@misc{labbe2026from,
title = {{From skew to reflected SPDEs}},
author = {Cyril Labbé and Thomas Le Guerch and Lorenzo Zambotti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13014},
eprint = {2609.13014},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13014},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From skew to reflected SPDEs
AU - Cyril Labbé
AU - Thomas Le Guerch
AU - Lorenzo Zambotti
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13014
UR - https://arxiv.org/abs/2609.13014
AB - In this article, we prove that the solution of the skew stochastic heat equation converges to the solution of the stochastic heat equation with reflection in the limit of infinite skewness. The result holds at equilibrium. This provides an SPDE analog of the link between skew and reflected Brownian motion. One of the intermediate results is the convergence in law of a penalised Brownian bridge to a 3-Bessel bridge.
ER -