5 citations · 6 across the 3 of their papers we have counts for
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Elementary fixed points of the BRW smoothing transforms with infinite number of summands
Aleksander M. Iksanov
The branching random walk (BRW) smoothing transform is defined as , where given realizations $\{X_{i}\}_{i…
On perpetuities related to the size-biased distributions
Aleksander M. Iksanov
We study perpetuities of a special type related to the size-biased distributions. Necessary and sufficient conditions of their existence and uniqueness are obtained. A crucial poin…
On fixed points of Poisson shot noise transforms
Aleksander M. Iksanov, Zbigniew J. Jurek
Distributional fixed points of a Poisson shot noise transform (for nonnegative, nonincreasing response functions bounded by 1) are characterized. The tail behavior of fixed points…
A new factorization property of the selfdecomposable probability measures
Aleksander M. Iksanov, Zbigniew J. Jurek, Bertram M. Schreiber
We prove that the convolution of a selfdecomposable distribution with its background driving law is again selfdecomposable if and only if the background driving law is s-selfdecomp…
New explicit examples of fixed points of Poisson shot noise transforms
Aleksander M. Iksanov, Che Soong Kim
We show that gamma distributions, generalized positive Linnik distributions, S2 distributions are fixed points of Poisson shot noise transforms. The corresponding response function…
Shot noise distributions and selfdecomposability
Aleksander M. Iksanov, Zbigniew J. Jurek
Stationary (limiting) distributions of shot noise processes, with exponential response functions, form a large subclass of positive selfdecomposable distributions that we illustrat…