A class of multivariate infinitely divisible distributions related to arcsine density

作者：Maejima Makoto^*; Perez Abreu Victor; Sato Ken Iti

来源：Bernoulli, 2012, 18(2): 476-495.

DOI：10.3150/10-BEJ348

• arcsine density
• class A
• general Upsilon transformation
• generalized type G distribution
• infinitely divisible distribution
• Levy measure

Two transformations A(1) and A(2) of Levy measures on R-d based on the arcsine density are studied and their relation to general Upsilon transformations is considered. The domains of definition of A(1) and A(2) are determined and it is shown that they have the same range. The class of infinitely divisible distributions on R-d with Levy measures being in the common range is called the class A and any distribution in the class A is expressed as the law of a stochastic integral integral(1)(0) cos(2(-1) pi t)dX(t) with respect to a Levy process {X-t}. This new class includes as a proper subclass the Jurek class of distributions. It is shown that generalized type G distributions are the image of distributions in the class A under a mapping defined by an appropriate stochastic integral. A(2) is identified as an Upsilon transformation, while A(1) is shown not to be.

• 出版日期2012-5