Tail estimates for stochastic fixed point equations via nonlinear renewal theory

This paper presents precise large deviation estimates for solutions to stochastic fixed point equations of the type V =_d f(V), where f(v) = Av + g(v) for a random function g(v) = o(v) a.s. as v tends to infinity. Specifically, we provide an explicit characterization of the pair (C,r) in the tail estimate P(V > u) ~ C u^-r as u tends to infinity, and also present a Lundberg-type upper bound of the form P(V > u)