## Tokyo Journal of Mathematics

### Cone-Parameter Convolution Semigroups and Their Subordination

#### Abstract

Convolution semigroups of probability measures with parameter in a cone in a Euclidean space generalize usual convolution semigroups with parameter in $[0,\infty)$. A characterization of such semigroups is given and examples are studied. Subordination of cone-parameter convolution semigroups by cone-valued cone-parameter convolution semigroups is introduced. Its general description is given and inheritance properties are shown. In the study the distinction between cones with and without strong bases is important.

#### Article information

Source
Tokyo J. Math., Volume 26, Number 2 (2003), 503-525.

Dates
First available in Project Euclid: 5 June 2009

https://projecteuclid.org/euclid.tjm/1244208605

Digital Object Identifier
doi:10.3836/tjm/1244208605

Mathematical Reviews number (MathSciNet)
MR2020800

Zentralblatt MATH identifier
1039.43004

#### Citation

PEDERSEN, Jan; SATO, Ken-iti. Cone-Parameter Convolution Semigroups and Their Subordination. Tokyo J. Math. 26 (2003), no. 2, 503--525. doi:10.3836/tjm/1244208605. https://projecteuclid.org/euclid.tjm/1244208605

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