Large Deviations for Processes with Independent Increments.

摘要

The establishment of the large deviation principle (LDP) has had important implications in various areas in statistics. It has been used to obtain the asymptotic efficiencies of tests and estimates and to obtain the asymptotic behavior of functional integrals associated with solutions of stochastic integrals. It appears in the evaluation of the 'free' energy in statistical mechanics. It is also intimately related to certain types of laws of large numbers. This paper studies the LDP for a stochastic process with stationary independent increments with no Gaussian component and obtain complete results.