A martingale view of Blackwell’s renewal theorem and its extensions to a general counting process
A martingale view of Blackwell’s renewal theorem and its extensions to a general counting process
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布莱克威尔更新定理及其对一般计数过程的扩展的鞅观点
DOI：
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发表时间：
2017
影响因子：
1
通讯作者：
M. Miyazawa
中科院分区：
文献类型：
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作者：
D. Daley;M. Miyazawa
摘要令是随机分析中的一个基本工具，本文考虑了它们在计数过程中的应用。我们用这个工具重温了一个更新定理，并给出了各种计数过程的推广。我们首先考虑更新过程作为一个试点例子，通过随机强度函数得到了不同于标准分解的新的半鞅表示。然后，我们重温布莱克韦尔的更新定理，它的改进和扩展。在此基础上，我们将半鞅表示推广到一般的计数过程，并给出了类似于Blackwell更新定理的渐近行为成立的条件。
Abstract Martingales constitute a basic tool in stochastic analysis; this paper considers their application to counting processes. We use this tool to revisit a renewal theorem and give extensions for various counting processes. We first consider a renewal process as a pilot example, deriving a new semimartingale representation that differs from the standard decomposition via the stochastic intensity function. We then revisit Blackwell’s renewal theorem, its refinements and extensions. Based on these observations, we extend the semimartingale representation to a general counting process, and give conditions under which asymptotic behaviour similar to Blackwell’s renewal theorem holds.
DOI：
10.1007/978-1-4419-9473-8
发表时间：
2011-01-01
期刊：
INTRODUCTION TO HEAVY-TAILED AND SUBEXPONENTIAL DISTRIBUTION
影响因子：
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作者：
Foss, Sergey;Korshunov, Dmitry;Zachary, Stan
通讯作者：
Zachary, Stan