Randomly stopped sums with consistently varying distributions
Copyright policy )Randomly stopped sums with consistently varying distributions
Let $\{ξ_1,ξ_2,\ldots\}$ be a sequence of independent random variables, and $η$ be a counting random variable independent of this sequence. We consider conditions for $\{ξ_1,ξ_2,\ldots\}$ and $η$ under which the distribution function of the random sum $S_η=ξ_1+ξ_2+\cdots+ξ_η$ belongs to the class of consistently varying distributions. In our consideration, the random variables $\{ξ_1,ξ_2,\ldots\}$ are not necessarily identically distributed.
Published at http://dx.doi.org/10.15559/16-VMSTA60 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)
- Vilnius University Lithuania
T57-57.97, Applied mathematics. Quantitative methods, Sums of independent random variables; random walks, random convolution closure., heavy tail, convolution closure, Probability (math.PR), randomly stopped sum, Extreme value theory; extremal stochastic processes, Convolution as an integral transform, consistently varying tail, Limit theorems in probability theory, QA1-939, FOS: Mathematics, random convolution closure, Heavy tail, Mathematics, inhomogeneous distributions, Mathematics - Probability
T57-57.97, Applied mathematics. Quantitative methods, Sums of independent random variables; random walks, random convolution closure., heavy tail, convolution closure, Probability (math.PR), randomly stopped sum, Extreme value theory; extremal stochastic processes, Convolution as an integral transform, consistently varying tail, Limit theorems in probability theory, QA1-939, FOS: Mathematics, random convolution closure, Heavy tail, Mathematics, inhomogeneous distributions, Mathematics - Probability
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