Abstract
In Palm theory it is very common to consider several distributions to describe the characteristics of the system. To study a stationary marked point process, the time-stationary distribution P and its event-stationary Palm distributions with respect to sets L of marks can all be used as starting point. When P is used, a modified, event-stationary version is defined as the limit of an obvious discrete-time Cesàro average. In a sense this modified Palm distribution is more natural than the ordinary one. When a Palm distribution is taken as starting point, we can approximate another modifiedevent-stationary version of by considering discrete-time Cesàro averages and a modifiedtime-stationary version QL of P by considering continuous-time Cesàro averages. These and other limit results are corollaries of uniform limit theorems for Cesàro averaged functionals. In essence, this paper presents a profound study of the relationship between and modified versions of them, and their connections with ergodicity conditions and long-run averages of Cesàro type.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
