Electronic Journal of Probability

Invariant measures for stochastic functional differential equations

Oleg Butkovsky and Michael Scheutzow

Full-text: Open access

Abstract

We establish new general sufficient conditions for the existence of an invariant measure for stochastic functional differential equations and exponential or subexponential convergence to the equilibrium. The obtained conditions extend the Veretennikov–Khasminskii conditions for SDEs and are optimal in a certain sense.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 98, 23 pp.

Dates
Received: 14 March 2017
Accepted: 29 October 2017
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1510802252

Digital Object Identifier
doi:10.1214/17-EJP122

Mathematical Reviews number (MathSciNet)
MR3724566

Zentralblatt MATH identifier
1382.34084

Subjects
Primary: 34K50: Stochastic functional-differential equations [See also , 60Hxx] 37L40: Invariant measures 60J60: Diffusion processes [See also 58J65]

Keywords
stochastic functional differential equations invariant measure Lyapunov function Veretennikov–Khasminskii condition

Rights
Creative Commons Attribution 4.0 International License.

Citation

Butkovsky, Oleg; Scheutzow, Michael. Invariant measures for stochastic functional differential equations. Electron. J. Probab. 22 (2017), paper no. 98, 23 pp. doi:10.1214/17-EJP122. https://projecteuclid.org/euclid.ejp/1510802252


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