| Affiliation: | (1) División Académica de Ciencias Básicas, UJAT, Apartado Postal 24, 86690 Cunduacán Tabasco, MÉXICO;(2) División Académica de Ciencias Básicas, UJAT, Apartado Postal 24, 86690 Cunduacán Tabasco, MÉXICO;(3) Departamento de Matemáticas, Facultad de Ciencias—UNAM, Cd. Universitaria, 04510 D. F., MÉXICO |
| Abstract: | In this paper we consider a system whose statex changes to  (x) if a perturbation occurs at the timet, for  . Moreover, the statex changes to the new state (x) at timet, for  . It is assumed that thenumber of perturbations in an interval (0,t) is a Poisson process. Here and are measurable maps from a measure space  into itself. We giveconditions for the existence of a stationary distribution of thesystem when the maps and commute, and we prove that anystationary distribution is an invariant measure of thesemaps. |
