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math.PR2002
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…
math.PR2002
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…
math.PR2001
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…