Mathematics – Probability
Scientific paper
2011-09-08
Mathematics
Probability
Scientific paper
Let $Z$ be a random variable with values in a proper closed convex cone $C\subset \R^d$, $A$ a random endomorphism of $C$ and $N$ a random integer. Given $N$ independent copies $(A_i,Z_i)$ of $(A,Z)$ we define a new random variable $\wh Z = \sum_{i=1}^N A_i Z_i$. Let $T$ be the corresponding transformation on the set of probability measures on $C$. We study existence and properties of fixed points of $T$. Previous one dimensional results on existence of fixed points of T as well as on homogeneity of their tails are extended to higher dimensions.
Buraczewski Dariusz
Damek Ewa
Guivarc'h Yves
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