节制时空分数负二项过程

arXiv - MATH - Probability Pub Date : 2024-09-11 DOI:arxiv-2409.07044

Shilpa, Ashok Kumar Pathak, Aditya Maheshwari

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引用次数: 0

摘要

本文通过将分数泊松过程与独立的回火米塔格-勒夫勒 L\'{e}vy 附属器进行附属，定义了回火时空分数负二项式过程（TSTFNBP）。我们研究了它的分布特性及其与偏微分方程的联系，并推导出其分数阶矩的渐近行为和长程依赖特性。结果表明，TSTFNBP 表现出过度离散性。我们还得到了一些与首过时间相关的结果。

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Tempered space-time fractional negative binomial process

In this paper, we define a tempered space-time fractional negative binomial process (TSTFNBP) by subordinating the fractional Poisson process with an independent tempered Mittag-Leffler L\'{e}vy subordinator. We study its distributional properties and its connection to partial differential equations. We derive the asymptotic behavior of its fractional order moments and long-range dependence property. It is shown that the TSTFNBP exhibits overdispersion. We also obtain some results related to the first-passage time.

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arXiv - MATH - Probability

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