General Criteria of Integrability of Functions of Passage-Times for Nonnegative Stochastic Processes and Their Applications
General Criteria of Integrability of Functions of Passage-Times for Nonnegative Stochastic Processes and Their Applications
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非负随机过程通道时间函数可积性的一般准则及其应用
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发表时间：
1999
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影响因子：
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通讯作者：
R. Iasnogorodski
中科院分区：
文献类型：
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作者：
S. Aspandiiarov;R. Iasnogorodski
在本文中，我们研究了具有离散参数的随机过程的首次通过时间到紧集和首次返回时间的函数的可积性问题。我们首先考虑一类具有负漂移的过程，其值在 $\bR_{+}$ 中，并为它们证明这些随机时间的函数可积的一般充分条件。这些条件是按照福斯特发起的鞅精神制定的，并概括了之前获得的相应结果。在本文的第二部分中，我们针对内部零漂移象限中的反射随机游走提出了类似的问题。应用第一部分的结果，我们得到了反射随机游走的第一通过时间和第一返回时间的某些函数的可积条件。获得的估计为之前的随机时间提供了相当清晰的结果，并补充了[S. Aspandiiarov 和 R. Iasnogorodski，非负传递时间的尾部......
In this paper we study the question of integrability of functions of the first passage-times into compact sets and first return-times for stochastic processes with discrete parameter. We consider first a class of processes with negative drifts taking values in $\bR_{+}$ and prove for them general sufficient conditions for integrability of functions of these random times. The conditions are formulated in a martingale spirit initiated by Foster and generalize corresponding results obtained earlier. In the second part of the paper we address a similar question for reflected random walks in a quadrant with zero-drift in the interior. Applying the results of the first part we get conditions for integrability of certain functions of the first passage-times and the first return-times for the reflected random walks. The obtained estimates provide quite sharp results for the former random times and complement the corresponding results in [S. Aspandiiarov and R. Iasnogorodski, Tails of passage-time for non-negative...