Two Results on Dual Excursions
Two Results on Dual Excursions
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双重游览的两个结果
DOI：
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发表时间：
1981
期刊：
影响因子：
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通讯作者：
M. Sharpe
中科院分区：
文献类型：
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作者：
R. Getoor;M. Sharpe
这篇论文是最近工作[5]的续篇。如文中所述，对于两个主要结果，假设在公共状态空间E上有一对X(广义{X})标准马尔可夫过程，该条件比通常的预解式的对偶性强得多.该条件相对于E上的某个σ-有限测度具有对偶密度.事实上，在[5]中证明了密度的对偶等价于与X有关的某些时空过程的经典对偶，(宽帽{X})。文[5]的主要结果是关于度量族Px，L，y的构造和性质，这些度量族被证明控制着X从给定的闭齐次可选集M的游程分布，条件是游程始于x，止于y，长度为L。上述陈述中“支配”的确切含义在文[5]的两种情况下给出。在第一种情况下，考虑由Maisonneuve定义的停止时间[8]。有关正式说明，请参见第3节。粗略地说，这样的停止时间对应于这样的规则，即在旅行期间停止的决定可能只基于旅行开始之前获得的信息，以及旅行的年龄过程。
This paper is a sequel to the recent work [5]. As in that paper, it is supposed for the two principal results that one is given a pair X,( widehat{X} ) of standard Markov processes on a common state space E having a dual density relative to some σ-finite measure on E. This condition is considerably stronger than the usual duality of resolvents. In fact, it was shown in [5] that duality of densities is equivalent to classical duality of certain space-time processes associated with X,( widehat{X} ). The main result of [5] concerned the construction and properties of families of measures P x,l,y which were shown to govern the distribution of excursions of X from a given closed homogeneous optional set M, conditional on the excursion starting at x, ending at y and having length l. The precise meaning of “govern” in the statement above was laid out in two situations in [5]. One considers the excursion straddling a stopping time T. In the first case, one considers the stopping times defined by Maisonneuve [8]. See §3 for a formal description. Roughly speaking, such stopping times correspond to rules where the decision to stop during an excursion may be based only on information available before the excursion began, and on the age process of the excursion.