Asymptotic Behaviour of the Empirical Distance Covariance for Dependent Data

Abstract We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption samples. In particular, we show almost sure convergence of measure with finite first moments, provided that samples form a strictly stationary and ergodic process. further result concerning distribution under absolute regularity extend these to certain types pseudometric spaces. process, derive general theorem degenerate V-statistics order 2 strong mixing condition.