EXTENDED AND CONDITIONAL VERSIONS OF THE PASTA PROPERTY
EXTENDED AND CONDITIONAL VERSIONS OF THE PASTA PROPERTY
复制标题
PASTA 特性的扩展版本和条件版本
DOI：
10.2307/1427556
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发表时间：
1990
影响因子：
1.2
通讯作者：
V. Schmidt
中科院分区：
文献类型：
--
作者：
D. König;V. Schmidt
讨论了两种类型的条件，确保具有嵌入点过程的随机过程的长期运行时间分数和长期事件分数之间的相等性。考虑对此等式声明的修改。在当前的文献中（参见下面的参考文献）可以观察到几条调查线，涉及泊松到达时间平均值（PASTA）这一事实的概括。粗略地说，用于证明此类结果的方法可以分为两类：（i）利用 Martingale 技术，其中假设嵌入点过程承认随机强度。 (ii) 考虑条件强度，包括 Korolyuk 意义上的局部特征，其中这些条件强度的存在要么是先验假设的，要么是通过存在足够丰富的状态空间正则子集族来确保的。我们在固定框架内讨论这两种方法。特别是，陈述了条件 PASTA 属性的一般形式。
Two types of conditions are discussed ensuring the equality between long-run time fractions and long-run event fractions of stochastic processes with embedded point processes. Modifications of this equality statement are considered. In the current literature (see the references below) several lines of investigation can be observed dealing with generalizations of the fact that Poisson Arrivals see time averages (PASTA). Roughly speaking, the methods used for proving such results can be divided into two classes: (i) Martingale techniques are exploited, where the embedded point process is assumed to admit a stochastic intensity. (ii) Conditional intensities are considered, including their local characterization in the sense of Korolyuk, where the existence of these conditional intensities is either assumed a priori or ensured by the existence of a sufficiently rich family of regular subsets of the state space. We discuss these two approaches within the stationary framework. In particular, a general form of the conditional PASTA property is stated.