Tail homogeneity of invariant measures of multidimensional stochastic recursions in a critical case |
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Authors: | Konrad Kolesko |
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Institution: | 1. Instytut Matematyczny, Uniwersytet Wroc?awski, pl. Grunwaldzki 2/4, 50-384, Wroc?aw, Poland
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Abstract: | We consider the stochastic recursion ${X_{n+1} = M_{n+1}X_{n} + Q_{n+1}, (n \in \mathbb{N})}$ , where ${Q_n, X_n \in \mathbb{R}^d }$ , M n are similarities of the Euclidean space ${ \mathbb{R}^d }$ and (Q n , M n ) are i.i.d. We study asymptotic properties at infinity of the invariant measure for the Markov chain X n under assumption ${\mathbb{E}{\log|M|]}=0}$ i.e. in the so called critical case. |
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