Sub-exponential convergence to equilibrium for Gaussian driven Stochastic Differential Equations with semi-contractive drift

Abstract : The convergence to the stationary regime is studied for Stochastic Differential Equations driven by an additive Gaussian noise and evolving in a semi-contractive environment, i.e. when the drift is only contractive out of a compact set but does not have repulsive regions. In this setting, we develop a synchronous coupling strategy to obtain sub-exponential bounds on the rate of convergence to equilibrium in Wasserstein distance. Then by a coalescent coupling close to terminal time, we derive a similar bound in total variation distance.
Type de document :
Pré-publication, Document de travail
2018
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Contributeur : Alexandre Richard <>
Soumis le : vendredi 30 mars 2018 - 16:02:05
Dernière modification le : vendredi 6 avril 2018 - 15:45:59

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  • HAL Id : hal-01755497, version 1
  • ARXIV : 1804.01348

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Fabien Panloup, Alexandre Richard. Sub-exponential convergence to equilibrium for Gaussian driven Stochastic Differential Equations with semi-contractive drift. 2018. 〈hal-01755497〉

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