Well-Posedness, Stability, and Sensitivities for Stochastic Delay Equations: A Generalized Coupling Approach
Probability
2018-08-21 v1
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
Cite
@article{arxiv.1808.06050,
title = {Well-Posedness, Stability, and Sensitivities for Stochastic Delay Equations: A Generalized Coupling Approach},
author = {Alexei Kulik and Michael Scheutzow},
journal= {arXiv preprint arXiv:1808.06050},
year = {2018}
}