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Nonlinearly perturbed regenerative processes and pseudo-stationary phenomena for stochastic systems

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  • Gyllenberg, Mats
  • Silvestrov, Dmitrii S.

Abstract

New types of mixed large deviation and ergodic theorems are obtained for nonlinearly perturbed regenerative processes, semi-Markov processes, and continuous-time Markov chains with absorption. Applications to the analysis of pseudo-stationary phenomena for stochastic systems are discussed. Examples related to models of population dynamics and highly reliable queuing systems are considered.

Suggested Citation

  • Gyllenberg, Mats & Silvestrov, Dmitrii S., 2000. "Nonlinearly perturbed regenerative processes and pseudo-stationary phenomena for stochastic systems," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 1-27, March.
    • Handle: RePEc:eee:spapps:v:86:y:2000:i:1:p:1-27
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    Cited by:

    1. Dmitrii Silvestrov & Sergei Silvestrov & Benard Abola & Pitos Seleka Biganda & Christopher Engström & John Magero Mango & Godwin Kakuba, 2021. "Perturbed Markov Chains with Damping Component," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 369-397, March.
    2. Jose Blanchet & Bert Zwart, 2010. "Asymptotic expansions of defective renewal equations with applications to perturbed risk models and processor sharing queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 311-326, October.
    3. Gyllenberg, Mats & S. Silvestrov, Dmitrii, 2000. "Cramer-Lundberg approximation for nonlinearly perturbed risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 75-90, February.

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