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Zbl 0561.60075
Liao, Ming
Riesz representation and duality of Markov processes. (English)
[A] Sémin. de probabilités XIX, Univ. Strasbourg 1983/84, Proc., Lect. Notes Math. 1123, 366-396 (1985).

[For the entire collection see Zbl 0549.00007.] \par Starting with a Hunt process X with a reference measure m and a potential density u(x,y) of X with respect to m satisfying certain conditions it is proved that any excessive function $f<\infty$ a.e. (m) allows a Riesz representation of the form $$ f(x)=h(x)+\int u(x,y)d\mu (y), $$ where h is harmonic and $\mu$ is a Radon measure. If $\mu$ does not charge a certain set Z, called the exceptional set, this representation is unique. This result extends earlier results due to {\it K. L. Chung} and {\it K. M. Rao}, Ann. Inst. Fourier 30, 167-198 (1980; Zbl 0424.31004). \par Using the Riesz representation the author constructs a right continuous strong dual process Y whose set of branching points is Z. This gives a sort of converse of the original result by Hunt, which establishes the Riesz representation of Markov processes under certain duality assumptions.
[B.Øksendal]

MSC 2000:: *60J45 Probabilistic potential theory

Keywords: Hunt process; reference measure; potential density; Riesz representation; Radon measure; exceptional set; duality assumptions

Citations: Zbl 0549.00007; Zbl 0424.31004

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