 
Summary: The large deviation principle for certain series
Miguel A. Arcones
July 27, 2004
Abstract
We study the large deviation principle for stochastic processes of the form
{
k=1 xk(t)k : t T}, where {k}
k=1 is a sequence of i.i.d.r.v.'s with mean zero and
xk(t) R. We present necessary and sufficient conditions for the large deviation princi
ple for these stochastic processes in several situations. Our approach is based in showing
the large deviation principle of the finite dimensional distributions and an exponen
tial asymptotic equicontinuity condition. In order to get the exponential asymptotic
equicontinuity condition, we derive new concentration inequalities, which are of inde
pendent interest.
1 Introduction
We study the large deviation principle for stochastic processes of the form {
k=1 xk(t)k :
t T}, where {k}
k=1 is a sequence of i.i.d.r.v.'s with mean zero, T is a parameter set
and xk(t) R. Our results apply when log(P{1 t}), t > 0, is either a convex or a
