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Explicit estimates for the asymptotics of subexponential infinitely divisible distribution functions. (English. Russian original) Zbl 0970.60021
Math. Notes 67, No. 2, 239-244 (2000); translation from Mat. Zametki 67, No. 2, 295-301 (2000).
Let \(F(x)\) be an infinitely divisible distribution such that \(F(x)=0\) for \(x<0\), and let \(q(x)\) be the corresponding spectral function. In a special case, when \(q(x)\) has in a sense slow and regular decay, the author obtains order-sharp estimates on the rate of decay of the difference \(|1-F(x)-q(x)|\).

MSC:
60E07 Infinitely divisible distributions; stable distributions
60E15 Inequalities; stochastic orderings
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