Tail calculus with remainder, applications to tail expansions for infinite order moving averages, randomly stopped sums, and related topics

Extremes

Volumn 7, Issue 4, 2004, Pages 337-365

  Barbe, Ph ^a   Mccormick, W P ^b  

^a CNRS   (France)

^b UNIVERSITY OF GEORGIA   (United States)

Author keywords

Asymptotic expansion; Convolution; Heavy tail; Infinite order moving averages; Limiting waiting time distribution; Randomly stopped sums

Indexed keywords

EID: 26444584359     PISSN: 13861999     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10687-004-3481-z     Document Type: Article

References (8)

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3. Cline, D., Estimation and Linear Prediction for Regression, Autoregression and ARMA with Infinite Variance Data, Ph.D. Thesis, Dept. of Statistics, Colorado State University, Fort Collins, 1983a.
4. Cline, D., Infinite Series of Random Variables with Regularly Varying Tails, Tech. Report 83-24, Insitute of Applied Mathematics and Statistics, University of British Columbia, Vancouver, 1983b.
5. Cohen, J.W., "On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue," Ann. Instil. Henri Poincaré, B 8, 255-263, (1972).
6. Mikosch, T. and Samorodnistsky, G., "The supremum of a negative drift random random walk with dependent heavy tailed steps," Ann. Appl. Probab. 10, 1025-1064, (2000).
7. Olver, F.W.J., Asymptotic and Special Functions, Academic Press, New York, 1974.
8. Resnick, S.I., Extreme Values, Regular Variation, and Point Processes, Springer, New York, 1987.