Simple conditions for mixing of infinitely divisible processes

Jan Rosinski and Tomasz Zak

Stochastic Processes and their Applications, 1996, vol. 61, issue 2, 277-288

Abstract: Let (Xt)t[epsilon]T be a real-valued, stationary, infinitely divisible stochastic process. We show that (Xt)t[epsilon]T is mixing if and only if Eei(Xt - X0) --> EeiX02, provided the Lévy measure of X0 has no atoms in 2[pi]Z. We also show that if (Xt)t[epsilon]T is given by a stochastic integral with respect to an infinitely divisible measure then the mixing of (Xt)t[epsilon]T is equivalent to the essential disjointness of the supports of the representing functions.

Keywords: Stationary; process; Infinitely; divisible; process; Mixing; Weak; mixing (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (6)

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