Large Deviation Principles for Random Walk Trajectories. III

Abstract

The present paper is a continuation of [Theory Probab. Appl., 57 (2013), pp. 1--27]. It consists of two sections. Section 6 presents results similar to those obtained in sections 4 and 5, but now in the space of functions of bounded variation with metric stronger than that of $\D$. In section 7 we obtain the so-called conditional large deviation principles for the trajectories of univariate random walks with a localized terminal value of the walk. As a consequence, we prove a version of Sanov's theorem on large deviations of empirical distributions.