Properties of Completely Monotone and Bernstein Functions Related to the Shape of Their Measures

Hristo Sendov; Shen Shan

Abstract

We are interested in Bernstein and Lévy measures having certain convexity-type properties. We thoroughly investigate how the shape of these measures results in various properties of the corresponding completely monotone and Bernstein functions. We hope that by understanding these connections one would be able to shed more light on the several conjectures posed in another paper of the authors ["New representation theorems for completely monotone and Bernstein functions with convexity properties on their measures", J. Theoretical Probability (2014), DOI 10.1007/s10959-014-0557-9].

Author information

Contact details are reproduced from the original publication and may be historical.

Hristo Sendov

Dept. of Statistical and Actuarial Sciences, Western University, 1151 Richmond Str., London, Ont., Canada N6A 5B7

hssendov@stats.uwo.ca

Shen Shan

Dept. of Statistical and Actuarial Sciences, Western University, 1151 Richmond Str., London, Ont., Canada N6A 5B7

sshan2@uwo.ca

Keywords

Bernstein function
completely monotone function
Bernstein measure
Lévy measure
harmonically convex function

Mathematics Subject Classification

26A48, 26D07; 30E20

Suggested citation

H. Sendov, S. Shan. “Properties of Completely Monotone and Bernstein Functions Related to the Shape of Their Measures.” Journal of Convex Analysis 23 (2016), No. 4, 981–1015.