Summary
Given a stochastic matrixP on the state spaceI an ordering for measures inI can be defined in the following way:Μ≺Ν iffΜ(f)≦Ν(f) for allf in a sufficiently rich subcone of the cone of positiveP-subharmonic functions. It is shown that, ifΜ, Ν are probability measures with Μ≺Ν, then in theP-process (X n)n≧0 havingΜ as initial distribution there exists a stopping timeΤ such thatX Τ is distributed according toΝ. In addition,Τ can be chosen in such a way, that for every positive subharmonicf withΝ(f)<∞ the submartingale (f(X Τ∧n))n≧0 is uniformly integrable.
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Rost, H. Darstellung einer Ordnung von Maßen durch Stoppzeiten. Z. Wahrscheinlichkeitstheorie verw Gebiete 15, 19–28 (1970). https://doi.org/10.1007/BF01041972
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DOI: https://doi.org/10.1007/BF01041972