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4 matches found
V: 23, 237-250, LNM 191 (1971)
MEYER, Paul-André
Travaux de H. Rost en théorie du balayage (Potential theory, Ergodic theory)
The filling scheme'' is a technique used in ergodic theory to prove Hopf's maximal Lemma and the Chacon-Ornstein theorem, studied in detail by H.~Rost (Zeit. für W-theorie, 15, 1970; Ann. Inst. Fourier, 21, 1971): it provides a solution to Skorohod's imbedding problem for measures on discrete time Markov processes. Here it is also used to prove Brunel's Lemma in pointwise ergodic theory
Comment: Extension to continuous time in Meyer 612. See also 806, 1012. A general survey on the Skorohod embedding problem is Ob\lój, Probab. Surv. 1, 2004
Keywords: Filling scheme, Brunel's lemma, Skorohod imbedding
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V: 24, 251-269, LNM 191 (1971)
MEYER, Paul-André
Solutions de l'équation de Poisson dans le cas récurrent (Potential theory, Markov processes)
The problem is to solve the Poisson equation for measures, $\mu-\mu P=\theta$ for given $\theta$, in the case of a recurrent transition kernel $P$. Here a filling scheme'' technique is used
Comment: The paper was motivated by Métivier (Ann. Math. Stat., 40, 1969) and is completely superseded by one of Revuz (Ann. Inst. Fourier, 21, 1971)
Keywords: Recurrent potential theory, Filling scheme, Harris recurrence, Poisson equation
Nature: Original
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VI: 12, 130-150, LNM 258 (1972)
MEYER, Paul-André
Le schéma de remplissage en temps continu, d'après H. Rost (Ergodic theory, Potential theory)
The work of H. Rost on the so-called discrete filling scheme was presented to the Seminar as 523. Here following Rost himself (Invent. Math., 14, 1971) the construction is extended to continuous time Markov processes. In the transient case, the results are translated in potential-theoretic language, and proved using techniques due to Mokobodzki. Then the general case follows from this result applied to a space-time extension of the semi-group
Comment: A general survey on the Skorohod embedding problem is Ob\lój, Probab. Surv. 1, 2004
Keywords: Filling scheme, Balayage of measures, Skorohod imbedding
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