Strong Feller Property and Irreducibility for Diffusions on Hilbert Spaces
Peszat, Szymon ; Zabczyk, Jerzy
Ann. Probab., Tome 23 (1995) no. 3, p. 157-172 / Harvested from Project Euclid
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It is shown that the transition semigroup $(P_t)_{t\geq0}$ corresponding to a nonlinear stochastic evolution equation is strong Feller and irreducible, provided the nonlinearities are Lipschitz continuous and the diffusion term is nondegenerate. This result ensures the uniqueness of the invariant measure for $(P_t)_{t\geq0}$.
Publié le : 1995-01-14
Classification:  Strong Feller property,  irreducible Markov semigroups,  invariant measures,  stochastic evolution equations,  60J35,  60H15,  60J25 
@article{1176988381,
     author = {Peszat, Szymon and Zabczyk, Jerzy},
     title = {Strong Feller Property and Irreducibility for Diffusions on Hilbert Spaces},
     journal = {Ann. Probab.},
     volume = {23},
     number = {3},
     year = {1995},
     pages = { 157-172},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176988381}
}

Peszat, Szymon; Zabczyk, Jerzy. Strong Feller Property and Irreducibility for Diffusions on Hilbert Spaces. Ann. Probab., Tome 23 (1995) no. 3, pp.  157-172. http://gdmltest.u-ga.fr/item/1176988381/