Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields

We obtain central limit theorems for stationary random fields employing a novel measure of dependence called θ-lex weak dependence. show that this notion is more general than strong mixing, is, it applies to broader class models. Moreover, we discuss hereditary properties and η-weak illustrate the possible applications notions study asymptotic fields. Our results apply mixed moving average (MMAF) ambit conditions such MMAF fields, with volatility field being an or p-dependent field, are weakly dependent. For all models mentioned above, give complete characterization their coefficients sufficient normality sample moments. Finally, explicit computations MSTOU processes analyze under which developed theory CARMA