Measures of Dependence For Processes in metric spaces

Abstract

The Wasserstein distance between conditional distributions and the p distance of Gray, Neuhoff and Shields [14] are used to give generalizations of the notions of E;-independence, almost block independence and the very weak Bernoulli property for processes with values in Polish spaces, thereby exploiting the underlying metric structure of the state space. We prove implications between different versions of these notions under moment conditions, as well as connections to the property of being a stationary coding of an i.i.d. sequence and the absolute regularity and strong mixing conditions. Also, we use a class of Markov processes to give some examples and counterexamples.

Keywords:

• Wasserstein distance
• distance
• weak dependence
• Markov processes
• conditional distributions

*Present address: Ferdinand-Miller-Platz 12a, D-8000 mnchen 2, Federal Republic of Germany.

*Present address: Ferdinand-Miller-Platz 12a, D-8000 mnchen 2, Federal Republic of Germany.

Notes

*Present address: Ferdinand-Miller-Platz 12a, D-8000 mnchen 2, Federal Republic of Germany.