Coming up from $-\infty$ for KPZ via stochastic control
Probability
2025-08-26 v1
Abstract
We derive a lower bound, independent of the initial condition, for the solution of the KPZ equation on the torus through its representation as the value function of a (conditional) stochastic control problem. With the same techniques, we also prove a bound for its oscillation, again independent of initial conditions, from which a Harnack type inequality for the rough heat equation (on the torus) can be obtained.
Keywords
Cite
@article{arxiv.2508.18140,
title = {Coming up from $-\infty$ for KPZ via stochastic control},
author = {Nicolas Perkowski and Carlos Villanueva Mariz},
journal= {arXiv preprint arXiv:2508.18140},
year = {2025}
}
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17 pages