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Sharp estimate of the mean exit time of a bounded domain in the zero white noise limit

Abstract : We prove a sharp asymptotic formula for the mean exit time from an open bounded domain D ⊂ R d for the overdamped Langevin dynamics dX t = −−f (X t)dt + √ 2ε dB t in the limit ε → 0 and in the case when D contains a unique non degenerate minimum of f and ∂ n f > 0 on ∂D. As a direct consequence, one obtains in the limit ε → 0, a sharp asymptotic estimate of the smallest eigenvalue of the operator L ε = −ε∆ + f · associated with Dirichlet boundary conditions on ∂D. The approach does not require f | ∂D to be a Morse function. The proof is based on results from [7,8] and a formula for the mean exit time from D introduced in the potential theoretic approach to metastability [4, 5].
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https://hal-enpc.archives-ouvertes.fr/hal-01643931
Contributeur : Boris Nectoux <>
Soumis le : mardi 21 novembre 2017 - 17:51:47
Dernière modification le : mercredi 12 mai 2021 - 03:22:15

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  • HAL Id : hal-01643931, version 1
  • ARXIV : 1710.07510

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Boris Nectoux. Sharp estimate of the mean exit time of a bounded domain in the zero white noise limit. Markov Processes And Related Fields, Polymat Publishing Company, 2020, 26 (3), pp.403-421. ⟨hal-01643931⟩

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