We are looking into solution of the stochastic fixed point equation X=AX+B with nonnenegative coefficients.
Primarily, we are interested in the behavior of the distribution of X around 0. In a recent paper it was shown that if B is an IED (inverse exponential decay) random variable, and A and B are PQD (positively quadrant dependent), then X is also an IED-random variable.
In this talk we will dive into the question about general solutions of this equation and will show what happens if A and B are not PQD. Specially, this will solve the equation that models the long term behavior of a Fleming-Viot type process. Joint work with K. Burdzy.