Document Type
Article
Subject Area(s)
Statistics
Abstract
Let X be a topological space and F denote the Borel σ-field in X. A family of probability measures {Pλ} is said to obey the large deviation principle (LDP) with rate function I(⋅) if Pλ(A) can be suitably approximated by exp{−λinfx∈AI(x)} for appropriate sets A in F. Here the LDP is studied for probability measures induced by stochastic processes with stationary and independent increments which have no Gaussian component. It is assumed that the moment generating function of the increments exists and thus the sample paths of such stochastic processes lie in the space of functions of bounded variation. The LDP for such processes is obtained under the weak∗-topology. This covers a case which was ruled out in the earlier work of Varadhan (1966). As applications, the large deviation principle for the Poisson, Gamma and Dirichlet processes are obtained.
Publication Info
Published in The Annals of Probability, Volume 15, Issue 2, 1987, pages 610-627.
© The Annals of Probability 1987, Scientific Research.
Lynch, J. & Sethuraman, J. (1987). Large Deviations for Processes with Independent Increments. The Annals of Probability, 15(2),610-627. doi:10.1214/aop/1176992161
Rights
© The Annals of Probability 1987, Scientific Research.
Lynch, J. & Sethuraman, J. (1987). Large Deviations for Processes with Independent Increments. The Annals of Probability, 15(2),610-627. doi:10.1214/aop/1176992161