One-sided Cauchy-Stieltjes Kernel Families

Details One-sided Cauchy-Stieltjes Kernel Families One-sided Cauchy-Stieltjes Kernel Families

2009-06-22

arxiv.org/abs/0906.4073v2

Journ. Theoret. Probab. 24 (2011) 577--594

Mathematics

Probability

Scientific paper

10.1007/s10959-010-0303-x

This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel in place of the celebrated exponential kernel of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded on one side. We illustrate the need for such an extension by showing that cubic pseudo-variance functions correspond to free-infinitely divisible laws without the first moment. We also determine the domain of means, advancing the understanding of Cauchy-Stieltjes kernel families also for compactly supported generating measures.

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