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Journals / Selçuk Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi / 2002 / Sayı: 20

Renewal processes and integral equations

Yenileme süreçleri ve integral denklemler

HALİL AYDOĞDU
CEMAL ATAKAN
Pages
91–97
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Depending on the monotone convergence of the obtained sequence of the functions with the help of this integral equation, some bounds are found for the variance function of the process.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, integral equations are considered such that their solution functions are dependent on the mean value function of a renewal process.
📊
Key Findings & Data:Then, an integral equation is given for the variance function of the process.
💡
Conclusion & Impact:Depending on the monotone convergence of the obtained sequence of the functions with the help of this integral equation, some bounds are found for the variance function of the process.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, integral equations are considered such that their solution functions are dependent on the mean value function of a renewal process. Then, an integral equation is given for the variance function of the process. Depending on the monotone convergence of the obtained sequence of the functions with the help of this integral equation, some bounds are found for the variance function of the process.

Özet

Bu çalışmada, çözüm fonksiyonu bir yenileme sürecinin ortalama değer fonksiyonuna bağlı olan integral denklemleri üzerinde durulmaktadır. Bir yenileme sürecinin varyans fonksiyonu için bir integral denklem elde edilir. Bu integral denklem yardımıyla tanımlanan fonksiyonlar dizisinin varyans fonksiyonuna monoton yakınsamasına bağlı olarak varyans fonksiyonu için bazı sınır fonksiyonları verilir.

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Cite This Article

AYDOĞDU, H., ATAKAN, C. (2002). Renewal processes and integral equations. Selçuk Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, Sayı: 20, 91–97. https://ajindex.com/articles/317629

References (5)

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  2. Karlin, S. and Taylor, H. M., A First Course in Stochastic Processes. Second edition. Academic Press. New York, (1975)
  3. Moiseiwitsch, B. L., Integral Equations. Longman Group Limited, New York, (1977)
  4. Aydoğdu, H., Yenileme Süreçlerinde İntegral Denklemler. Yüksek Lisans Tezi, Ankara Üniversitesi Fen Bilimleri Enstitüsü, (1990)
  5. Xie, M., “Some results on the renewal equations.” Commun. Statist. Theory Meth. 18(3), 1159-1171, (1989).