weak dependence

Introductary talk to continuous-time locally stationary processes.

We establish asymptotic properties of M-estimator based on observations from a continuous-time locally stationary process. Simulation studies show the applicability of the estimation procedures.

We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use θ-weak dependence to establish laws of large numbers and central limit type results under different observation schemes.

We obtain central limit theorems for stationary random fields employing a novel measure of dependence called θ-lex weak dependence. Our general results apply to mixed moving average fields (MMAF in short) and ambit fields.