On the Regularity of Distribution for a Solution of SDE of a Jump Type with Arbitrary Levy Measure of the Noise
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.
English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 9, pp 1477-1501.
Citation Example: 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. Mat. Zh. - 2005. - 57, № 9. - pp. 1261–1283.