Stochastic fixed point equation and local dependence measure

We study solutions to the stochastic fixed point equation $XAX+B$ where the coefficients $A$ and $B$ are nonnegative random variables. We introduce the ``local dependence measure’’ (LDM) and its Legendre-type transform to analyze the left tail behavior of the distribution of $X$. We discuss the relationship of LDM with earlier results on the stochastic fixed point equation and we apply LDM to prove a theorem on a Fleming-Viot-type process.