Large deviations for processes on half-line

Abstract

We consider a sequence of processes X_n(t)$ defined on half-line $0\leq t<\infty$. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with metric $\rho(f,g)=\sup_{t\geq0} |f(t)−g(t)|/(1+t^{1+\kappa})$, $\kappa\geq0$. LDP is established for Random Walks, Diffusions, and CEV model of ruin, all defined on the half-line. LDP in this space is "more precise" than that with the usual metric of uniform convergence on compacts.