Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614577 | Journal of Mathematical Analysis and Applications | 2016 | 24 Pages |
Abstract
The problem of existence and uniqueness of absolutely continuous invariant measures for a class of piecewise deterministic Markov processes is investigated using the theory of substochastic semigroups obtained through the Kato–Voigt perturbation theorem on the L1L1-space. We provide a new criterion for the existence of a strictly positive and unique invariant density for such processes. The long time qualitative behavior of the corresponding semigroups is also considered. To illustrate our general results we give a detailed study of a two dimensional model of gene expression with bursting.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Weronika Biedrzycka, Marta Tyran-Kamińska,