A COUPLING BETWEEN RANDOM WALKS IN RANDOM ENVIRONMENTS AND BROX'S DIFFUSION - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

A COUPLING BETWEEN RANDOM WALKS IN RANDOM ENVIRONMENTS AND BROX'S DIFFUSION

Résumé

It has been established in [27] that a properly rescaled version of Sinai's random walk converges in distribution to Brox's diffusion. In this article we quantify this convergence by considering a specific coupling between Sinai's walk and Brox's diffusion. Our method relies on convergence results for martingale problems considered in the rough path setting.

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Dates et versions

hal-04752807 , version 1 (25-10-2024)

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Xi Geng, Mihai Gradinaru, Samy Tindel. A COUPLING BETWEEN RANDOM WALKS IN RANDOM ENVIRONMENTS AND BROX'S DIFFUSION. 2024. ⟨hal-04752807⟩
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