Open Access
2012 On temporally completely monotone functions for Markov processes
Francis Hirsch, Marc Yor
Probab. Surveys 9: 253-286 (2012). DOI: 10.1214/11-PS179


Any negative moment of an increasing Lamperti process(Yt,t0) is a completely monotone function of t. This property enticed us to study systematically, for a given Markov process (Yt,t0), the functions f such that the expectation of f(Yt) is a completely monotone function of t. We call these functions temporally completely monotone (for Y). Our description of these functions is deduced from the analysis made by Ben Saad and Janßen, in a general framework, of a dual notion, that of completely excessive measures. Finally, we illustrate our general description in the cases when Y is a Lévy process, a Bessel process, or an increasing Lamperti process.


Download Citation

Francis Hirsch. Marc Yor. "On temporally completely monotone functions for Markov processes." Probab. Surveys 9 253 - 286, 2012.


Published: 2012
First available in Project Euclid: 10 May 2012

zbMATH: 1245.60071
MathSciNet: MR2947802
Digital Object Identifier: 10.1214/11-PS179

Primary: 60J25 , 60J45
Secondary: 60G18 , 60J35

Keywords: completely excessive function , completely superharmonic function , Lamperti process , Lamperti’s correspondence , Markov process , Temporally completely monotone function

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.9 • 2012
Back to Top