Selfdecomposability and Semi-selfdecomposability in Subordination of Cone-parameter Convolution Semigroups

Selfdecomposability and Semi-selfdecomposability in Subordination of Cone-parameter Convolution Semigroups

Ken-iti SATO

Source: Tokyo J. of Math. Volume 32, Number 1 (2009), 81-90.

Abstract

Extension of two known facts concerning subordination is made. The first fact is that, in subordination of $1$-dimensional Brownian motion with drift, selfdecomposability is inherited from subordinator to subordinated. This is extended to subordination of cone-parameter convolution semigroups. The second fact is that, in subordination of strictly stable cone-parameter convolution semigroups on $\mathbf{R}^d$, selfdecomposability is inherited from subordinator to subordinated. This is extended to semi-selfdecomposability.

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Permanent link to this document: http://projecteuclid.org/euclid.tjm/1249648410
Digital Object Identifier: doi:10.3836/tjm/1249648410
Zentralblatt MATH identifier: 05604236
Mathematical Reviews number (MathSciNet): MR2541155

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