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Invariant measures for stochastic functional differential equations

2017; Institute of Mathematical Statistics; Volume: 22; Issue: none Linguagem: Inglês

10.1214/17-ejp122

1083-6489

Oleg Butkovsky, Michael Scheutzow,

advanced mathematical theories

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.