Asymptotics of the generalized renewal functions when the variance is finite

Theory of Probability and its Applications

Volumn 42, Issue 3, 1997, Pages 536-541

  Sgibnev, M S ^a  

^a ENERGY SYSTEMS INSTITUTE   (Russian Federation)

Author keywords

Generalized renewal functions; Higher renewal moments; Ladder epochs; Random walk

Indexed keywords

EID: 0031314126     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0040585x97976374     Document Type: Article

References (10)

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2. W. L. SMITH, On the cumulants of renewal processes. Biometrika, 46 (1959), pp. 1-29.
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4. W. FELLER, An Introduction to Probability Theory and Its Applications, Vol. 2, Wiley, New York, 1966.
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6. J. KIEFER AND J. WOLFOWITZ, On the characteristics of the general queueing process, with applications to random walk, Ann. Math. Statist., 27 (1956), pp. 147-161.
7. A. A. BOROVKOV, Stochastic Processes in Queueing Theory, Springer-Verlag, Berlin, New York, 1976.
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9. D. J. DALEY AND N. R. MOHAN, Asymptotic behaviour of the variance of renewal processes and random walks, Ann. Probability, 6 (1978), pp. 516-521.
10. W. L. SMITH, On some general renewal theorems for nonidentically distributed variables, in Proc. 4th Berkeley Sympos. Math. Statist. Probability, Vol. II (1961), pp. 467-514.