Large Deviations for processes on half-line

TL;DR

This paper establishes a more sensitive Large Deviation Principle (LDP) for processes on the half-line, providing improved precision over traditional uniform metrics, with applications to random walks, diffusions, and ruin models.

Contribution

It introduces a new metric for LDP on the half-line, enhancing the understanding of process deviations at infinity, applicable to various stochastic models.

Findings

LDP holds under new metric for processes on half-line

LDP is more precise than uniform convergence on compacts

Applicable to random walks, diffusions, and ruin models

Abstract

We consider a sequence of processes defined on half-line for all non negative t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with a new metric that is more sensitive to behaviour at infinity than the uniform metric. 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.