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Stationary Solutions of the Stochastic Differential Equation dV t =V t -dU t +dL t with Levy Noise

Behme, Anita; Lindner, Alexander; Maller, Ross


For a given bivariate Lvy process (Ut,Lt)t<0, necessary and sufficient conditions for the existence of a strictly stationary solution of the stochastic differential equation dVt=Vt-dUt+dLt are obtained. Neither strict positivity of the stochastic exponential of U nor independence of V0 and (U,L) is assumed and non-causal solutions may appear. The form of the stationary solution is determined and shown to be unique in distribution, provided it exists. For non-causal solutions, a sufficient...[Show more]

CollectionsANU Research Publications
Date published: 2011
Type: Journal article
Source: Stochastic Processes and their Applications
DOI: 10.1016/


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