No. 1021

Title:

Polynomial type large deviation inequalities and convergence of statistical random fields

Author(s):

Yoshida, Nakahiro (University of Tokyo);

Key words:

large deviation; weak convergence; Bayes estimator; stochastic differential equation.

Abstract:

We prove a certain polynomial type large deviation inequality for a statistical random field. From this result, it is possible to obtain weak convergence of the statistical random field, and asymptotic properties of statistics related to it. We apply those results to quasi-likelihood analysis for sampled stochastic differential equations. It turns out that Yury Kutoyants' scheme to apply Ibragimov-Hasminskii's theory to stochastic processes works for general stochastic differential equations.