Let $Z_0(t)$ be a Markov chain and $X(t)$ a subordinator. Set $Z(t) = Z_0(X(t))$ and let $\alpha$ be a nonstable state of $Z_0$. It is shown, via an example, that it is possible for $\alpha$ to be a stable state of $Z(t)$ even when the total mass of the Levy measure of $X$ is unbounded.
@article{1176995806,
author = {Rubinovitch, Michael},
title = {Can a Nonstable State Become Stable by Subordination?},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 463-466},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995806}
}
Rubinovitch, Michael. Can a Nonstable State Become Stable by Subordination?. Ann. Probab., Tome 5 (1977) no. 6, pp. 463-466. http://gdmltest.u-ga.fr/item/1176995806/