صندلی اداری

ON THE SMOOTHNESS OF PDF OF SOLUTIONS TO SDE OF JUMP TYPE

Takashi Komatsu, Atsushi Takeuchi

Abstract


Some regularities of marginal distributions of solutions to a SDE with jumps are investigated via the Malliavin calculus on the c\'{a}d-l\'{a}g space. A key lemma on the estimation of some functionals of semimartingales is obtained. Using the lemma, the H\"{o}rmander theorem on the hypoellipticity is generalized to a theorem for the integro-differential operator associated with the SDE.

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