Normal Deviation of Gamma Processes in Random Environment With Applications

IF 1.3 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Applied Stochastic Models in Business and Industry Pub Date : 2025-01-30 DOI:10.1002/asmb.2929

Nikolaos Limnios

引用次数: 0

Abstract

We consider gamma processes of homogeneous type, which live in a random environment or media represented by a pure jump Markov process. The aim of this paper is to approximate such gamma processes by a diffusion. Since gamma processes are increasing, the diffusion approximation requires an average approximation first. This averaged process will serve as an equilibrium to the initial gamma process. We present two main results: averaging and normal deviation. An application for degradation systems in reliability modeling is discussed.

查看原文本刊更多论文

随机环境中伽马过程的正态偏差及其应用

我们考虑存在于随机环境或纯跳跃马尔可夫过程所表示的介质中的齐次过程。本文的目的是用扩散来近似这种伽马过程。由于伽马过程是递增的，扩散近似首先需要一个平均近似。这个平均过程将作为初始过程的平衡。我们给出了两个主要结果：平均和正态偏差。讨论了退化系统在可靠性建模中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Stochastic Models in Business and Industry 数学-数学跨学科应用

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.