Multiplicative monotonic convolution

Hari Bercovici

doi:10.1215/ijm/1258138229

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Home > Journals > Illinois J. Math. > Volume 49 > Issue 3 > Article

Fall 2005 Multiplicative monotonic convolution

Hari Bercovici

Illinois J. Math. 49(3): 929-951 (Fall 2005). DOI: 10.1215/ijm/1258138229

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Abstract

We show that the monotonic independence introduced by Muraki can also be used to define a multiplicative convolution. We also find a method for the calculation of this convolution based on an appropriate form of the Cauchy transform. Finally, we discuss infinite divisibility in the multiplicative monotonic context.