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On the Regularity of Distribution for a Solution of SDE of a Jump Type with Arbitrary Levy Measure of the Noise

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Abstract

The local properties of distributions of solutions of SDE's with jumps are studied. Using the method based on the “time-wise” differentiation on the space of functionals of Poisson point measure, we give a full analog of Hormander condition, sufficient for the solution to have a regular distribution. This condition is formulated only in terms of coefficients of the equation and does not require any regularity properties of the Levy measure of the noise.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, Ukraine

    A. M. Kulik

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  1. A. M. Kulik
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Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 9, pp. 1261–1283, September, 2005.

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Kulik, A.M. On the Regularity of Distribution for a Solution of SDE of a Jump Type with Arbitrary Levy Measure of the Noise. Ukr Math J 57, 1477–1501 (2005). https://doi.org/10.1007/s11253-006-0008-6

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  • DOI: https://doi.org/10.1007/s11253-006-0008-6

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