Densities for Ornstein-Uhlenbeck processes with jumps |
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Authors: | Priola, Enrico Zabczyk, Jerzy |
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Affiliation: | Dipartimento di Matematica Universitàdi Torino via Carlo Alberto 10 10123 Torino Italy |
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Abstract: | We consider an Ornstein–Uhlenbeck process with valuesin n driven by a Lévy process (Zt) taking values in dwith d possibly smaller than n. The Lévy noise can havea degenerate or even vanishing Gaussian component. Under a controllabilityrank condition and a mild assumption on the Lévy measureof (Zt), we prove that the law of the Ornstein–Uhlenbeckprocess at any time t > 0 has a density on n. Moreover, whenthe Lévy process is of -stable type, (0, 2), we showthat such density is a C-function. |
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