NDLI: Central Limit Theorems for Volume and Surface Content of Stationary Poisson Cylinder Processes in Expanding Domains

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Central Limit Theorems for Volume and Surface Content of Stationary Poisson Cylinder Processes in Expanding Domains

Content Provider	Scilit
Author	Heinrich, Lothar Spiess, Malte
Copyright Year	2013
Description	A stationary Poisson cylinder process in the d-dimensional Euclidean space is composed of a stationary Poisson process of k-flats (0 ≤ k ≤ d−1) which are dilated by independent and identically distributed random compact cylinder bases taken from the corresponding (d−k)-dimensional orthogonal complement. If the second moment of the (d−k)-volume of the typical cylinder base exists, we prove asymptotic normality of the d-volume of the union set of Poisson cylinders that covers an expanding star-shaped domain ϱ W as ϱ grows unboundedly. Due to the long-range dependencies within the union set of cylinders, the variance of its d-volume in ϱ W increases asymptotically proportional to the (d+k) th power of ϱ. To obtain the exact asymptotic behaviour of this variance, we need a distinction between discrete and continuous directional distributions of the typical k-flat. A corresponding central limit theorem for the surface content is stated at the end.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B88223228A543BFDD767F4C760812FF3/S0001867800006340a.pdf/div-class-title-central-limit-theorems-for-volume-and-surface-content-of-stationary-poisson-cylinder-processes-in-expanding-domains-div.pdf
Ending Page	331
Page Count	20
Starting Page	312
ISSN	00018678
e-ISSN	14756064
DOI	10.1017/s0001867800006340
Journal	Advances in Applied Probability
Issue Number	02
Volume Number	45
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	2013-06-01
Access Restriction	Open
Subject Keyword	Advances in Applied Probability Mathematical Physics Statistics and Probability Independently Marked Poisson Process Truncated Typical Cylinder Direction Space Volume Fraction Moment Convergence Theorem Asymptotic Variance range Dependence order (mixed) Cumulant
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistics and Probability

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