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II: 05, 75-110, LNM 51 (1968)
GIROUX, Gaston
Théorie des frontières dans les chaînes de Markov (Markov processes)
A presentation of the theory of Markov chains under the hypothesis that all states are regular
Comment: This is the subject of the short monograph of Chung, Lectures on Boundary Theory for Markov Chains, Princeton 1970
Keywords: Markov chains, Boundary theory
Nature: Exposition
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II: 11, 175-199, LNM 51 (1968)
MEYER, Paul-André
Compactifications associées à une résolvante (Potential theory)
Let $E$ be a locally compact space, $(U_p)$ be a submarkovian resolvent, with a potential kernel $U=U_0$ which maps $C_k$ (the continuous functions with compact support) into continuous bounded functions. Let $F$ be a compact space containing $E$ as a dense subset, but inducing possibly a coarser topology. It is assumed that all potentials $Uf$ with $f\in C_k$ extend to continuous functions on $F$, and that points of $F$ are separated by continuous functions on $F$ whose restriction to $E$ is supermedian. Then it is shown how to extend the resolvent to $F$ and imitate the construction of a Ray semigroup and a strong Markov process. This was an attempt to compactify the space using only supermedian functions, not $p$-supermedian for all $p>0$. An application to Markov chains is given
Comment: This method of compactification suggested by Chung's boundary theory for Markov chains (similarly Doob, Trans. Amer. Math. Soc., 149, 1970) never superseded the standard Ray-Knight approach
Keywords: Resolvents, Ray compactification, Martin boundary, Boundary theory
Nature: Original
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