Abstract
A stationary Poisson cylinder process (d;k) cyl is composed of a stationary Poisson process ofk-flats in R d that are dilated by i.i.d. random compact cylinder bases taken from the corresponding orthogonal complement. We study the accuracy of normal approximation of thed-volumeV (d;k) % of the union set of (d;k) cyl that covers%W as the scaling factor % becomes large. Here W is some fixed compact star-shaped set containing the origin as an inner point. We give lower and upper bounds of the variance of V (d;k) % that exhibit long-range dependence within the union set of cylinders. Our main results are sharp estimates of the higher-order cumulants of V (d;k) % under the assumption that the (d k)-volume of the typical cylinder base possesses a finite exponential moment. These estimates enable us to apply the celebrated Lemma on large deviations of Statuleviˇ cius. MSC: primary 60D05, 60F05; secondary 60F10, 60G55
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 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.
