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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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Submitted on : Tuesday, June 2, 2020 - 10:44:04 PM
Last modification on : Sunday, November 29, 2020 - 6:48:02 PM

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Fabien Panloup, Alexandre Richard. Sub-exponential convergence to equilibrium for Gaussian driven Stochastic Differential Equations with semi-contractive drift. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2020, 25, ⟨10.1214/20-EJP464⟩. ⟨hal-01755497v3⟩

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