Well-Posedness, Stability, and Sensitivities for Stochastic Delay Equations: A Generalized Coupling Approach

Alexei Kulik; Michael Scheutzow

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arXiv · 1808.06050

Well-Posedness, Stability, and Sensitivities for Stochastic Delay Equations: A Generalized Coupling Approach

Alexei Kulik·Michael Scheutzow

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Abstract

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

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Alexei Kulik, Michael Scheutzow. 2018-08-18. Well-Posedness, Stability, and Sensitivities for Stochastic Delay Equations: A Generalized Coupling Approach. https://arxiv.org/abs/1808.06050

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