Translator Disclaimer
November 2020 Well-posedness, stability and sensitivities for stochastic delay equations: A generalized coupling approach
Alexei Kulik, Michael Scheutzow
Ann. Probab. 48(6): 3041-3076 (November 2020). DOI: 10.1214/20-AOP1449

Abstract

We develop a new generalized coupling approach to the study of stochastic delay equations with Hölder 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.

Citation

Download Citation

Alexei Kulik. Michael Scheutzow. "Well-posedness, stability and sensitivities for stochastic delay equations: A generalized coupling approach." Ann. Probab. 48 (6) 3041 - 3076, November 2020. https://doi.org/10.1214/20-AOP1449

Information

Received: 1 September 2018; Revised: 1 February 2020; Published: November 2020
First available in Project Euclid: 20 October 2020

MathSciNet: MR4164460
Digital Object Identifier: 10.1214/20-AOP1449

Subjects:
Primary: 34K50, 60H25, 60J25

Rights: Copyright © 2020 Institute of Mathematical Statistics

JOURNAL ARTICLE
36 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.48 • No. 6 • November 2020
Back to Top