Logarithmic asymptotics in Queueing Theory and Risk Theory

Abstract

This thesis addresses four distinct, but related, problems. All four involve large deviation theory. The first problem is to relate the logarithmic asymptotics of the single server queue length distribution to the long time-scale large deviations of the stochastic driving force. Sufficient conditions are presented under which this relationship has a simple form, even in the presence of nonlinear scales