This article is cited in 2 scientific papers (total in 2 papers)
On the distribution of multiple power series regularly varying at the boundary point
A. L. Yakymiv
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Let $B(x)$ be a multiple power series with nonnegative coefficients which is convergent for all $x\in(0,1)^n$ and diverges at the point $\mathbf1=(1,…,1)$. Random vectors (r.v.) $\xi_x$ such that $\xi_x$ has distribution of the power series $B(x)$ type is studied. The integral limit theorem for r.v. $\xi_x$ as $x\uparrow\mathbf1$ is proved under the assumption that $B(x)$ is regularly varying at this point. Also local version of this theorem is obtained under the condition that the coefficients of the series $B(x)$ are one-sided weakly oscillating at infinity.
Multiple power series distribution, weak convergence, $\sigma$-finite measures, gamma-distribution, regularly varying functions, one-sided weakly oscillating functions
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Discrete Mathematics and Applications, 2019, 29:6, 409–421
A. L. Yakymiv, “On the distribution of multiple power series regularly varying at the boundary point”, Diskr. Mat., 30:3 (2018), 141–158; Discrete Math. Appl., 29:6 (2019), 409–421
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\paper On the distribution of multiple power series regularly varying at the boundary point
\jour Diskr. Mat.
\jour Discrete Math. Appl.
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This publication is cited in the following articles:
A. L. Yakymiv, “Abelian theorem for the regularly varying measure and its density in orthant”, Theory Probab. Appl., 64:3 (2019), 385–400
L. Yakymiv, A., “Local limit theorem for the multiple power series distributions”, Mathematics, 8:11 (2020), 2067
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