Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes

Alexander Lindner and Ross Maller

Stochastic Processes and their Applications, 2005, vol. 115, issue 10, 1701-1722

Abstract: The generalised Ornstein-Uhlenbeck process constructed from a bivariate Lévy process ([xi]t,[eta]t)t[greater-or-equal, slanted]0 is defined aswhere V0 is an independent starting random variable. The stationarity of the process is closely related to the convergence or divergence of the Lévy integral . We make precise this relation in the general case, showing that the conditions are not in general equivalent, though they are for example if [xi] and [eta] are independent. Characterisations are expressed in terms of the Lévy measure of ([xi],[eta]). Conditions for the moments of the strictly stationary distribution to be finite are given, and the autocovariance function and the heavy-tailed behaviour of the stationary solution are also studied.

Keywords: Generalised; Ornstein-Uhlenbeck; process; Lévy; integral; Stochastic; integral; Strict; stationarity; Autocovariance; function; Heavy-tailed; behaviour (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (16)

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