Abstract:For an increasing sequence (Tn) of one-parameter semigroups of sub Markovian kernel operators over a Polish space, we study the limit semigroup and prove sufficient conditions for it to be strongly Feller. In particular, we show that the strong Feller property carries over from the approximating semigroups to the limit semigroup if the resolvent of the latter maps 1 to a continuous function.This is instrumental in the study of elliptic operators on R d with unbounded coefficients: our abstract result enables u… Show more
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