Abstract
We derive asymptotic expansions for tails of infinite weighted convolutions of some heavy-tailed distributions. Applications are given to tail expansion of the marginal distribution of ARMA processes, randomly stopped sums, as well as limiting waiting time distribution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barbe, Ph. and McCormick, W.P., “Asymptotic expansions of convolutions of regularly varying distributions,” J. Austr. Math. Soc. 78, 339–371, (2005).
Bingham, N.H., Goldie, C.M., and Teugels, J.L., Regular Variation, Cambridge University Press, Cambridge, 1987.
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.
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.
Cohen, J.W., “On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue,” Ann. Instit. Henri Poincaré, B 8, 255–263, (1972).
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).
Olver, F.W.J., Asymptotic and Special Functions, Academic Press, New York, 1974.
Resnick, S.I., Extreme Values, Regular Variation, and Point Processes, Springer, New York, 1987.
Author information
Authors and Affiliations
Corresponding author
Additional information
AMS 2000 Subject Classifications. Primary—62E99, Secondary—41A60, 44A35, 60G50, 60K25
Rights and permissions
About this article
Cite this article
Barbe, P., McCormick, W.P. Tail Calculus with Remainder, Applications to Tail Expansions for Infinite Order Moving Averages, Randomly Stopped Sums, and Related Topics. Extremes 7, 337–365 (2004). https://doi.org/10.1007/s10687-004-3481-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10687-004-3481-z