Necessary conditions in limit theorems for cumulative processes
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.
Year of publication: |
2002
|
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Authors: | Glynn, Peter W. ; Whitt, Ward |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 98.2002, 2, p. 199-209
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Publisher: |
Elsevier |
Keywords: | Central limit theorem Markov chains Regenerative processes Cumulative processes Random sums Law of large numbers |
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