J. Rosinski et T. Zak, SIMPLE CONDITIONS FOR MIXING OF INFINITELY DIVISIBLE PROCESSES, Stochastic processes and their applications, 61(2), 1996, pp. 277-288
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.