  We study solutions to the stochastic fixed point equation
$X\stackrel{d}{=}AX+B$ 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.
