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Coming up from $-\infty$ for KPZ via stochastic control
Nicolas Perkowski, Carlos Villanueva Mariz · 2025-08-25 · via math.PR updates on arXiv.org

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.

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