Coming up from $-\infty$ for KPZ via stochastic control

Fuente: arXiv
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Main Authors: Perkowski, Nicolas, Mariz, Carlos Villanueva
Format: Preprint
Published: 2025
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_version_ 1866918130247270400
author Perkowski, Nicolas
Mariz, Carlos Villanueva
author_facet Perkowski, Nicolas
Mariz, Carlos Villanueva
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_18140
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Coming up from $-\infty$ for KPZ via stochastic control
Perkowski, Nicolas
Mariz, Carlos Villanueva
Probability
60H17, 60H15, 60L40
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.
title Coming up from $-\infty$ for KPZ via stochastic control
topic Probability
60H17, 60H15, 60L40
url https://arxiv.org/abs/2508.18140