One-point extensions of Markov processes by darning
نویسندگان
چکیده
This paper is a continuation of the works by Fukushima-Tanaka [14] and Chen-FukushimaYing [8] on the study of one-point extendability of a pair of standard Markov processes in weak duality. In this paper, general conditions to ensure such an extension are given. In the symmetric case, characterizations of the one-point extensions are given in terms of their Dirichlet forms and in terms of their L-infinitesimal generators. In particular, a generalized notion of flux is introduced and is used to characterize functions in the domain of the L-infinitesimal generator of the extended process. An important role in our investigation is played by the α-order approaching probability uα.
منابع مشابه
One-point extensions of locally compact paracompact spaces
A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...
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