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.
Citation
Ken-iti SATO. "Selfdecomposability and Semi-selfdecomposability in Subordination of Cone-parameter Convolution Semigroups." Tokyo J. Math. 32 (1) 81 - 90, June 2009. https://doi.org/10.3836/tjm/1249648410
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