Alexei Kulik, Michael Scheutzow
Published 2018-08-18Version 1
We develop a new generalized coupling approach to the study of stochastic delay equations with H\"older continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak solutions, and establish weak ergodic rates for the corresponding segment processes. We also prove, under additional smoothness assumptions on the coefficients, stabilization rates for the sensitivities in the initial value of the corresponding semigroups
Asymptotic coupling and a weak form of Harris' theorem with applications to stochastic delay equations
A generalized coupling approach for the weak approximation of stochastic functional differential equations
Duality and the well-posedness of a martingale problem
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