Invariant measures for stochastic functional differential equations with superlinear drift term. (English) Zbl 1240.34396
Summary: We consider a stochastic functional differential equation with an arbitrary Lipschitz diffusion coefficient depending on the past. The drift part contains a term with superlinear growth and satisfying a dissipativity condition. We prove tightness and Feller property of the segment process to show the existence of an invariant measure.
MSC:
| 34K50 | Stochastic functional-differential equations |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60H20 | Stochastic integral equations |
| 47D07 | Markov semigroups and applications to diffusion processes |
