Abstract
The present paper continues the work by Davidson, Krickeberg, Papangelou, and the author on proving, under weakest possible assumptions, that a stationary random measure η or a simple point process ξ on the space of k-flats in R d is a.s. invariant or a Cox process respectively. The problems for ξ and η are related by the fact that ξ is Cox whenever the Papangelou conditional intensity measure ζ of (a thinning of) ξ is a.s. invariant. In particular, η is shown to be a.s. invariant, whenever it is absolutely continuous with respect to some fixed measure μ and has no (so called) outer degeneracies. When k=d−2≧2, no absolute continuity is needed, provided that the first moments exist and that η has no inner degeneracies either. Under a certain regularity condition on ξ, it is further shown that ξ and ζ are simultaneously non-degenerate in either sense.
Sign-in/Register to access full text options 
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 callMore From: Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete
Disclaimer: 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.
