Abstract
We establish some asymptotic expansions for infinite weighted convolutions of distributions having rapidly varying subexponential tails. Examples are presented, some showing that in order to obtain an expansion with two significant terms, one needs to have a general way to calculate higher order expansions, due to possible cancellations of terms. An algebraic methodology is employed to obtain the results.
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Barbe, P., McCormick, W.P. Asymptotic expansions for infinite weighted convolutions of rapidly varying subexponential distributions. Probab. Theory Relat. Fields 141, 155–180 (2008). https://doi.org/10.1007/s00440-007-0082-1
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DOI: https://doi.org/10.1007/s00440-007-0082-1
Keywords
- Asymptotic expansion
- Convolution
- Tail area approximation
- Regular variation
- Subexponential distributions
- Infinite order moving average
- Weighted sum of random variables