The large deviation principle for certain series
Department of Mathematical Sciences, Binghamton University,
Binghamton, NY 13902, USA; firstname.lastname@example.org.
We study the large deviation principle for stochastic processes of the form , where is a sequence of i.i.d.r.v.'s with mean zero and . We present necessary and sufficient conditions for the large deviation principle for these stochastic processes in several situations. Our approach is based in showing the large deviation principle of the finite dimensional distributions and an exponential asymptotic equicontinuity condition. In order to get the exponential asymptotic equicontinuity condition, we derive new concentration inequalities, which are of independent interest.
Mathematics Subject Classification: 60F10
Key words: Large deviations / stochastic processes.
© EDP Sciences, SMAI, 2004