Distributional properties of solutions of $dV_t = V_{t-}dU_t + dL_t$ with Lévy noise

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  • Anita Behme - , Technical University of Braunschweig (Author)


For a given bivariate Levy process (Ut,Lt )t>0, distributional properties of the stationary solutions of the stochastic differential equation dVt = Vt-dUt + dL t are analysed. In particular, the expectation and autocorrelation function are obtained in terms of the process (U,L) and in several cases of interest the tail behavior is described. In the case where U has jumps of size -1, necessary and sufficient conditions for the law of the solutions to be (absolutely) continuous are given.


Original languageEnglish
Pages (from-to)688-711
JournalAdvances in Applied Probability
Issue number3
Publication statusPublished - 2011
Externally publishedYes

External IDs

Scopus 80053430747


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