Large Deviations for Processes with Independent Increments

摘要: 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 large deviation principle (LDP) with rate function $I(\cdot)$ if $P_\lambda(A)$ can suitably approximated by $\exp\{-\lambda \inf_{x\in A}I(x)\}$ for appropriate sets $A$ $\mathscr{F}$. Here LDP studied induced stochastic processes stationary independent increments which have no Gaussian component. It assumed that moment generating exists thus sample paths such lie functions bounded variation. The obtained under weak$^\ast$-topology. This covers case was ruled out earlier work Varadhan (1966). As applications, Poisson, Gamma Dirichlet are obtained.