The Distribution of the First Hit for Stable and Asymptotically Stable Walks on an Interval
The Distribution of the First Hit for Stable and Asymptotically Stable Walks on an Interval
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区间上稳定和渐近稳定游走的首次命中的分布
DOI：
10.1137/1117035
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发表时间：
1973
影响因子：
0.6
通讯作者：
B. A. Rogozin
中科院分区：
文献类型：
--
作者：
B. A. Rogozin
1.文[1]-[5]研究了对称稳定过程从有限区间通过时的首击分布。本文将文[4]和[5]中的结论推广到强稳定过程的情形。反过来，后者的结果允许建立一个极限定理的分布的第一次击中渐近稳定行走的间隔。在[4]和[5]中，我们已经考虑了整数格上对称渐近稳定游动的问题。2.设{（t），>= 0}是指数为a的强稳定过程.我们假设的样本路径是右连续的，概率为1。我们用Px（Ex）表示在（0）x条件下对应于过程的概率（数学期望）.指数为a的强稳定性的前提是过程的增量在不相交区间上的独立性，并且对任意t2> t1-> _ 0，（t2）-（t1）与（t2 t）/（（1）（0））同分布.对于强稳定过程（且仅对它们）
1. The distribution of the first hit in passing from a finite interval for symmetric stable proc-cesses has been studied in [1]-[5]. In this paper, by a generalization of the arguments of [4] and [5], these results are extended to the case of strongly stable processes. In turn the latter results permit a limittheorem to be established for the distribution of the first hit for asymptotically stable walks on an interval. Earlier in [4] and [5] this problem had been considered for symmetric asymptotically stable walks onan integer lattice. 2. Let{(t),>= 0} be a strongly stable process with exponent a. We shall assume that the sample paths of is right-continuous with probability 1. We denote by Px (Ex), the probability (mathematical expectation) corresponding to theprocess under the condition that (0) x.The property of strong stability of with exponent a presupposes independence of the increments of the process on disjoint intervals, and also that, for any t2> tl-> _ 0,(t2)-(tl) is identically distributed with (t2 t)/((1)(0)). For strongly stable processes (and only for them)