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

2018/04/04 by Panloup, Fabien, Richard, Alexandre
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1804.01348

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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