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April, 1987 Large Deviations for Processes with Independent Increments
James Lynch, Jayaram Sethuraman
Ann. Probab. 15(2): 610-627 (April, 1987). DOI: 10.1214/aop/1176992161


Let $\mathscr{X}$ be a topological space and $\mathscr{F}$ denote the Borel $\sigma$-field in $\mathscr{X}$. A family of probability measures $\{P_\lambda\}$ is said to obey the large deviation principle (LDP) with rate function $I(\cdot)$ if $P_\lambda(A)$ can be suitably approximated by $\exp\{-\lambda \inf_{x\in A}I(x)\}$ for appropriate sets $A$ in $\mathscr{F}$. 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$^\ast$-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.


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James Lynch. Jayaram Sethuraman. "Large Deviations for Processes with Independent Increments." Ann. Probab. 15 (2) 610 - 627, April, 1987.


Published: April, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0624.60045
MathSciNet: MR885133
Digital Object Identifier: 10.1214/aop/1176992161

Primary: 60F10
Secondary: 60E07 , 60J30

Keywords: Dirichlet process , large deviations , Rate function , stationary and independent increments

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 2 • April, 1987
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