Limit Theorems for Monotonic Convolution and the Chernoff Product Formula Academic Article uri icon

abstract

  • Bercovici and Pata showed that the correspondence between classically, freely, and Boolean infinitely divisible distributions holds on the level of limit theorems. We extend this correspondence also to distributions infinitely divisible with respect to the additive monotone convolution. Because of noncommutativity of this convolution, we use a new technique based on the Chernoff product formula. We also study this correspondence for multiplicative monotone convolution, where the Bercovici-Pata bijection no longer holds. © 2013 The Author(s) 2013. Published by Oxford University Press. All rights reserved.

author list (cited authors)

  • Anshelevich, M., & Williams, J. D.

citation count

  • 2

publication date

  • March 2013