Electronic Journal of Probability

Invariant measures for stochastic functional differential equations

Oleg Butkovsky and Michael Scheutzow

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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

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

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

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

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

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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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