广义计数过程的时变变体

IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY Journal of Applied Probability Pub Date : 2023-10-27 DOI:10.1017/jpr.2023.70
M. Khandakar, K. K. Kataria
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引用次数: 0

摘要

摘要本文利用一个独立的逆混合稳定从属子对广义计数过程(GCP)进行时变,得到了GCP的分数型。我们称之为混合分数计数过程(MFCP)。用Z变换方法得到了控制其状态概率的分数阶微分方程组。得到了其一维分布、均值、方差、协方差、概率生成函数和阶乘矩。结果表明,MFCP具有长程依赖特性,而其增量过程具有短程依赖特性。作为一个应用,我们考虑一个风险过程,其中索赔是使用MFCP建模的。对于该风险过程,我们得到了其有限时间破产概率在索赔规模为亚指数分布且初始资本为任意大时的渐近行为。随后,我们讨论了复合GCP的一些分布性质。
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On a time-changed variant of the generalized counting process
Abstract In this paper, we time-change the generalized counting process (GCP) by an independent inverse mixed stable subordinator to obtain a fractional version of the GCP. We call it the mixed fractional counting process (MFCP). The system of fractional differential equations that governs its state probabilities is obtained using the Z transform method. Its one-dimensional distribution, mean, variance, covariance, probability generating function, and factorial moments are obtained. It is shown that the MFCP exhibits the long-range dependence property whereas its increment process has the short-range dependence property. As an application we consider a risk process in which the claims are modelled using the MFCP. For this risk process, we obtain an asymptotic behaviour of its finite-time ruin probability when the claim sizes are subexponentially distributed and the initial capital is arbitrarily large. Later, we discuss some distributional properties of a compound version of the GCP.
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来源期刊
Journal of Applied Probability
Journal of Applied Probability 数学-统计学与概率论
CiteScore
1.50
自引率
10.00%
发文量
92
审稿时长
6-12 weeks
期刊介绍: Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.
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