PreprintCC BY 4.0arXiv
Stochastic heat equations with non-Lipschitz coefficients driven by symmetric α-stable Lévy white noise
Abstract
We study the stochastic heat equation on a bounded interval with zero Dirichlet boundary conditions, driven by symmetric α-stable space--time Lévy white noise, where 1<α<2. Both the drift and noise coefficients are continuous and have at most linear growth. For bounded deterministic initial data and every r>1/2, we construct a weak solution with càdlàg paths in the negative Sobolev space ℍ−r. We also construct a predictable mild solution on the same stochastic basis and with the same noise. At each fixed deterministic time, this mild solution is a density of the distribution-valued weak solution.
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BibTeX
@misc{jimenez2026stochastic,
title = {{Stochastic heat equations with non-Lipschitz coefficients driven by symmetric $α$-stable Lévy white noise}},
author = {Juan J. Jiménez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04895},
eprint = {2610.04895},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04895},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stochastic heat equations with non-Lipschitz coefficients driven by symmetric α-stable Lévy white noise
AU - Juan J. Jiménez
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.04895
UR - https://arxiv.org/abs/2610.04895
AB - We study the stochastic heat equation on a bounded interval with zero Dirichlet boundary conditions, driven by symmetric α-stable space--time Lévy white noise, where 1<α<2. Both the drift and noise coefficients are continuous and have at most linear growth. For bounded deterministic initial data and every r>1/2, we construct a weak solution with càdlàg paths in the negative Sobolev space ℍ_−r. We also construct a predictable mild solution on the same stochastic basis and with the same noise. At each fixed deterministic time, this mild solution is a density of the distribution-valued weak solution.
ER -