Stationary Solutions of the Stochastic Differential Equation dV t =V t -dU t +dL t with Levy Noise
- Behme, Anita
- Lindner, Alexander
- Maller, Ross
Publication date
February 2016
DOI Publisher
Elsevier BV Journal
Stochastic Processes and their ApplicationsAbstract
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 condition for U and L to remain semimartingales with respect to the corresponding expanded filtration is given
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