ABSOLUTE CONTINUITY CONDITIONS FOR MULTIVARIATE INFINITELY DIVISIBLE DISTRIBUTIONS AND THEIR APPLICATIONS

作者：Yamazato M^*

来源：Theory of Probability and Its Applications, 2012, 56(2): 299-312.

DOI：10.1137/S0040585X97985406

• absolute continuity
• multivariate infinitely divisible distributions
• type processes

Two sufficient conditions for absolute continuity with respect to the Lebesgue measure of multivariate infinitely divisible distributions are given. These conditions are applied for proofs of absolute continuity of infinitely divisible distributions whose Levy measures have generalized polar decomposition with absolutely continuous radial part (GPDACR), defined in section 4 of the paper. Moreover, one of the conditions is applied to a proof of necessary and sufficient condition for the absolute continuity of transition probabilities of OU-type processes driven by Levy processes.

• 出版日期2012