 
Summary: The large deviation principle of
stochastic processes 1
Miguel A. Arcones
Department of Mathematical Sciences
Binghamton University
Binghamton, NY 139026000
arcones@math.binghamton.edu
Abstract
We discuss the large deviation principle of stochastic processes as
random elements of l(T). We show that the large deviation princi
ple in l(T) is equivalent to the large deviation principle of the finite
dimensional distributions plus an exponential asymptotic equicontinu
ity condition with respect to a pseudometric which makes T a totally
bounded pseudometric space. This result allows to obtain necessary
and sufficient conditions for the large deviation principle of different
types of stochastic processes. We discuss the large deviation principle
of Gaussian and Poisson processes. As application, we determine the
integrability of the iterated fractional Brownian motion.
April 13, 2004
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