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Iterated random functions and regularly varying tails

ABSTRACT We consider solutions to so-called stochastic fixed point equation , where Ψ is a random Lipschitz function and R is a random variable independent of Ψ. Under the assumption that Ψ can be approximated by the function , we show that the tail of R is comparable with the one of A, provided that the distribution of is tail equivalent. In particular, we obtain new results for the random difference equation.