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Probabilistic large deviations approach to obstacle Hamilton-Jacobi equations
Abstract
In this paper, we derive a non-classical variational representation of a viscosity solution of a Hamilton-Jacobi equation with obstacle, in which the Hamiltonian may take infinite values. We study a nonlinear selection-mutation model with an exponential-decay mutation kernel, using a probabilistic Feynman-Kac representation of a pure jump process. To handle the singular character of this process, we rely on a non-standard tool from large deviations theory, which allows us to establish a Varadhan-type lemma. This, in turn, yields the variational representation of the viscosity solution.
Related
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BibTeX
@misc{jeddi2026probabilistic,
title = {{Probabilistic large deviations approach to obstacle Hamilton-Jacobi equations}},
author = {Anouar Jeddi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24724},
eprint = {2610.24724},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24724},
}
RIS
TY - UNPB
TI - Probabilistic large deviations approach to obstacle Hamilton-Jacobi equations
AU - Anouar Jeddi
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24724
UR - https://arxiv.org/abs/2610.24724
AB - In this paper, we derive a non-classical variational representation of a viscosity solution of a Hamilton-Jacobi equation with obstacle, in which the Hamiltonian may take infinite values. We study a nonlinear selection-mutation model with an exponential-decay mutation kernel, using a probabilistic Feynman-Kac representation of a pure jump process. To handle the singular character of this process, we rely on a non-standard tool from large deviations theory, which allows us to establish a Varadhan-type lemma. This, in turn, yields the variational representation of the viscosity solution.
ER -