A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence of a unique stationary density and give sufficient conditions for asymptotic stability.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-2, author = {Michael C. Mackey and Marta Tyran-Kami\'nska}, title = {Dynamics and density evolution in piecewise deterministic growth processes}, journal = {Annales Polonici Mathematici}, volume = {93}, year = {2008}, pages = {111-129}, zbl = {1183.47038}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-2} }
Michael C. Mackey; Marta Tyran-Kamińska. Dynamics and density evolution in piecewise deterministic growth processes. Annales Polonici Mathematici, Tome 93 (2008) pp. 111-129. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-2/