Resumo:
This work is divided into two chapters. In the 竡rst chapter, we provide an introduction
to the theory of large deviations and prove a weak Large Deviation Principle (LDP) for
the empirical measure of the random walk with certain rates. To achieve this, we use the
Parabolic Anderson Model (PAM) and the Gärtner-Ellis Theorem. In the second chapter
we show that the empirical measure of certain continuous time random walks satis竡es a
strong large deviation principle with respect to a topology introduced in [21] by Mukherjee
and Varadhan. This topology is natural in models which exhibit an invariance with respect
to spatial translations. Our result applies in particular to the case of simple random walk
and complements the results obtained in [21] in which the large deviation principle has
been established for the empirical measure of Brownian motion.
