Coming up from $-\infty$ for KPZ via stochastic control
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918130247270400 |
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| 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 |