Stationary Solutions of the Stochastic Differential Equation
نویسندگان
چکیده
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 dVt = Vt− dUt + dLt are obtained. Neither strict positivity of the stochastic exponential of U nor independence of V0 and (U,L) are assumed and noncausal solutions may appear. The form of the stationary solution is determined and shown to be unique in distribution, provided it exists. For noncausal solutions, a sufficient condition for U and L to remain semimartingales with respect to the corresponding expanded filtration is given.
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