SIMPLE CONDITIONS FOR MIXING OF INFINITELY DIVISIBLE PROCESSES

Let (X(t))(t is an element of T) be a real-valued, stationary, infinit ely divisible stochastic process. We show that (X(t))(t is an element of T) is mixing if and only if Ee(i(Xt-X0)) --> \Ee(1X0)\(2) , provide d the Levy measure of X(0) has no atoms in 2 pi Z. We also show that i f (X(t))(t is an element of)T is given by a stochastic integral with r espect to an infinitely divisible measure then the mixing of (X(t))(t is an element of)T is equivalent to the essential disjointness of the supports of the representing functions.