Stationary solutions of the stochastic differential equation with Lévy noise

Anita Behme, Alexander Lindner and Ross Maller

Stochastic Processes and their Applications, 2011, vol. 121, issue 1, 91-108

Abstract: For a given bivariate Lévy process (Ut,Lt)t>=0, necessary and sufficient conditions for the existence of a strictly stationary solution of the stochastic differential equation 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 condition for U and L to remain semimartingales with respect to the corresponding expanded filtration is given.

Keywords: Stochastic; differential; equation; Lévy; process; Generalized; Ornstein-Uhlenbeck; process; Stochastic; exponential; Stationarity; Non-causal; Filtration; expansion (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (4)

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