The notion of a finitely determined process of Ornstein (see e.g. Ornstein (1974)) and Schwarz (1980) is generalized for processes in Polish spaces by using the distance of Gray, Neuhoff and Shields (1975) and it is related to some notions of asymptotic independence.
distance information number finitely determined almost block independent very weak Bernoulli absolutely regular stationary coding of an i.i.d. sequence Markov processes