Open Access
2017 Invariant measures for stochastic functional differential equations
Oleg Butkovsky, Michael Scheutzow
Electron. J. Probab. 22: 1-23 (2017). DOI: 10.1214/17-EJP122


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.


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Oleg Butkovsky. Michael Scheutzow. "Invariant measures for stochastic functional differential equations." Electron. J. Probab. 22 1 - 23, 2017.


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

zbMATH: 1382.34084
MathSciNet: MR3724566
Digital Object Identifier: 10.1214/17-EJP122

Primary: 34K50 , 37L40 , 60J60

Keywords: invariant measure , Lyapunov function , Stochastic functional differential equations , Veretennikov–Khasminskii condition

Vol.22 • 2017
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