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The large deviation principle for certain series Miguel A. Arcones
 

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

  

Source: Arcones, Miguel A. - Department of Mathematical Sciences, State University of New York at Binghamton

 

Collections: Mathematics