TL;DR
This paper characterizes total positivity in space-time for real strictly stable semigroups, solving longstanding problems and analyzing properties of stable densities across various cases.
Contribution
It provides a comprehensive characterization of total positivity in stable semigroups, addressing open questions and extending previous studies.
Findings
Total positivity characterized for positive stable semigroups.
Resolved a problem raised by Karlin regarding total positivity.
Analyzed bell-shape and monotone likelihood properties of stable densities.
Abstract
We characterize the total positivity in space-time of real strictly stable semigroups. In the positive case, this solves a problem which had been raised by Karlin. In the drifted Cauchy case, this concludes a study which we had initiated in a previous paper. The case of isotropic stable semigroups is also investigated. We apply these results to the bell-shape and monotone likelihood properties of certain real stable densities.
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