## Iterated random functions and regularly varying tails. (arXiv:1706.03876v1 [math.PR])

We consider solutions to so-called stochastic fixed point equation \$R \stackrel{d}{=} \Psi(R)\$, where \$\Psi \$ is a random Lipschitz function and \$R\$ is a random variable independent of \$\Psi\$. Under the assumption that \$\Psi\$ can be approximated by the function \$x \mapsto Ax+B\$ we show that the tail of \$R\$ is comparable with the one of \$A\$, provided that the distribution of \$\log (A\vee 1) \$ is tail equivalent. In particular we obtain new results for the random difference equation. 查看全文>>