Large Deviations for Processes on Half-Line: Random Walk and Compound Poisson

Abstract

We establish, under the Cramer exponential moment condition in a neighbourhood of zero, the Extended Large Deviation Principle for the Random Walk and the Compound Poisson processes in the metric space $\V$ of functions of finite variation on $[0,\infty )$ with the modified Borovkov metric $\r(f,g)= \r_\B(\hat{f},\hat{g}) $, where $\hat{f}(t)=f(t)/(1+t)$, $t\in \mathbb{R}$, and $\r_\B$ is the Borovkov metric. LDP in this space is "more precise" than that with the usual metric of uniform convergence on compacts.

arXiv comment20 pages