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2020 Sub-exponential convergence to equilibrium for Gaussian driven Stochastic Differential Equations with semi-contractive drift
Fabien Panloup, Alexandre Richard
Electron. J. Probab. 25(none): 1-43 (2020). DOI: 10.1214/20-EJP464

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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Fabien Panloup. Alexandre Richard. "Sub-exponential convergence to equilibrium for Gaussian driven Stochastic Differential Equations with semi-contractive drift." Electron. J. Probab. 25 1 - 43, 2020. https://doi.org/10.1214/20-EJP464

Information

Received: 6 June 2019; Accepted: 3 May 2020; Published: 2020
First available in Project Euclid: 2 June 2020

zbMATH: 07225516
MathSciNet: MR4112766
Digital Object Identifier: 10.1214/20-EJP464

Subjects:
Primary: 37A25, 60G15, 60G22

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