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Sub-exponential convergence to equilibrium for Gaussian driven stochastic differential equations with semi-contractive drift. (English) Zbl 1462.60046
Summary: 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.
60G15 Gaussian processes
60G22 Fractional processes, including fractional Brownian motion
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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