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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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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

Retrieve article from Numdam