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VIII: 06, 27-36, LNM 381 (1974)
DINGES, Hermann
Stopping sequences (Markov processes, Potential theory)
Given a discrete time Markov process $(X_n)$ with transition kernel $P$, a stopping sequence with initial distribution $\mu$ is a family $(\mu_n)$ of measures such that $\mu\ge\mu_0$ and $\mu_{k-1}P\ge\mu_k$. The stopping sequence associated with a stopping time $T$ is the sequence of distributions of $X_{T}, k< T<\infty$ under the law $P_\mu$. Every stopping sequence arises in this way from some randomized stopping time $T$, and the distribution of $X_T, T<\infty$ is independent of $T$ and called the final distribution. Then several constructions of stopping sequences are described, including Rost's filling scheme'', and several operations on stopping sequences, aiming at the construction of short'' stopping times in the Skorohod imbedding problem, without assuming transience of the process
Comment: This is a development of the research of H.~Rost on the filling scheme'', for which see 523, 524, 612. This article contains announcements of further results
Keywords: Discrete time Markov processes, Skorohod imbedding, Filling scheme
Nature: Original
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