Regularly Varying Multiple Power Series and it's Distributions
A. L. Yakymiv
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
A multiple power series $B(x)$ with non-negative coefficients converging in $x\in(0,1)^n$ and diverging at the point $\mathbf1=(1,…,1)$ is considered. A random variable (r.v.) $\xi_x$ having power series distribution $B(x)$ is studied. The integral limit theorem for r.v. $\xi_x$ as $x\uparrow\mathbf1$ is proved under the assumption that $B(x)$ regularly varies at this point. Also local version of this theorem is received in the situation when the coefficients of the series $B(x)$ are one-sided weakly oscillatory at infinity.
Multiple power series distribution, weak convergence of $\sigma$-finite measures and random vectors, gamma-distribution with parameter $\lambda\geq0$, regularly varying and one-sided weakly oscillatory functions in a positive hyper-octant.
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A. L. Yakymiv, “Regularly Varying Multiple Power Series and it's Distributions”, Diskr. Mat., 30:3 (2018), 141–158
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\paper Regularly Varying Multiple Power Series and it's Distributions
\jour Diskr. Mat.
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