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Necessary conditions in limit theorems for cumulative processes

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  • Glynn, Peter W.
  • Whitt, Ward

Abstract

We show that sufficient conditions in terms of moments for cumulative processes (additive functionals of regenerative processes) to satisfy the central limit theorem and the weak law of large numbers established in Glynn and Whitt (Stochastic Process. Appl. 47 (1993) 299-314) are also necessary, as previously conjectured.

Suggested Citation

  • Glynn, Peter W. & Whitt, Ward, 2002. "Necessary conditions in limit theorems for cumulative processes," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 199-209, April.
    • Handle: RePEc:eee:spapps:v:98:y:2002:i:2:p:199-209
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    1. Glynn, Peter W. & Whitt, Ward, 1993. "Limit theorems for cumulative processes," Stochastic Processes and their Applications, Elsevier, vol. 47(2), pages 299-314, September.
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    Cited by:

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    2. Jeffrey P. Kharoufeh & Dustin G. Mixon, 2009. "On a Markov‐modulated shock and wear process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 563-576, September.
    3. Liu, Jinpeng & Liu, Yuanyuan & Zhao, Yiqiang Q., 2022. "Augmented truncation approximations to the solution of Poisson’s equation for Markov chains," Applied Mathematics and Computation, Elsevier, vol. 414(C).

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