Classes of time-dependent measures, non-homogeneous Markov processes, and Feynman-Kac propagators

Gulisashvili, Archil

doi:10.1090/S0002-9947-08-04492-9

Classes of time-dependent measures, non-homogeneous Markov processes, and Feynman-Kac propagators
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Trans. Amer. Math. Soc. 360 (2008), 4063-4098 Request permission

Abstract:

We study the inheritance of properties of free backward propagators associated with transition probability functions by backward Feynman-Kac propagators corresponding to functions and time-dependent measures from non-autonomous Kato classes. The inheritance of the following properties is discussed: the strong continuity of backward propagators on the space $L^r$, the $(L^r-L^q)$-smoothing property of backward propagators, and various generalizations of the Feller property. We also prove that a propagator on a Banach space is strongly continuous if and only if it is separately strongly continuous and locally uniformly bounded.

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