Abstract:
The paper examines the expansion of the strictly stable law for $x\to0$ and $x\to\infty$ in the case of extreme values of the asymmetry parameter. Asymptotic expansions of the probability density and distribution functions are obtained, as well as estimates of the residual terms of these expansions. Based on the obtained estimates of the residual terms, a criterion is presented that allows determining the coordinate region within which it is possible to use these asymptotic expansions. The presented calculations confirm the validity of the obtained expressions.
Keywords:stable law, expansion of stable law, probability density, distribution function, Laplace method, asymptotic expansion, Bell polynomial.
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