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.
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Contributor : Alexandre Richard <>
Submitted on : Wednesday, June 19, 2019 - 12:24:12 PM
Last modification on : Friday, June 21, 2019 - 1:32:36 AM

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  • HAL Id : hal-01755497, version 2
  • 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. 2019. ⟨hal-01755497v2⟩

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