Tail Calculus with Remainder, Applications to Tail Expansions for Infinite Order Moving Averages, Randomly Stopped Sums, and Related Topics
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.
Key wordsasymptotic expansion convolution heavy tail infinite order moving averages limiting waiting time distribution randomly stopped sums
Unable to display preview. Download preview PDF.
- Barbe, Ph. and McCormick, W.P., “Asymptotic expansions of convolutions of regularly varying distributions,” J. Austr. Math. Soc. 78, 339–371, (2005).Google Scholar
- Bingham, N.H., Goldie, C.M., and Teugels, J.L., Regular Variation, Cambridge University Press, Cambridge, 1987.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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).Google Scholar
- Olver, F.W.J., Asymptotic and Special Functions, Academic Press, New York, 1974.Google Scholar
- Resnick, S.I., Extreme Values, Regular Variation, and Point Processes, Springer, New York, 1987.Google Scholar