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September 2011 Distributional properties of solutions of dVt = Vt-dUt + dLt with Lévy noise
Anita Diana Behme
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Adv. in Appl. Probab. 43(3): 688-711 (September 2011). DOI: 10.1239/aap/1316792666

Abstract

For a given bivariate Lévy process (Ut, Lt)t≥0, distributional properties of the stationary solutions of the stochastic differential equation dVt = Vt-dUt + dLt 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.

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Anita Diana Behme. "Distributional properties of solutions of dVt = Vt-dUt + dLt with Lévy noise." Adv. in Appl. Probab. 43 (3) 688 - 711, September 2011. https://doi.org/10.1239/aap/1316792666

Information

Published: September 2011
First available in Project Euclid: 23 September 2011

MathSciNet: MR2858217
Digital Object Identifier: 10.1239/aap/1316792666

Subjects:
Primary: 60G10, 60G51

Rights: Copyright © 2011 Applied Probability Trust

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Vol.43 • No. 3 • September 2011
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