On weak stationarity and weak isotropy of processes of convex bodies and cylinders
2007 ◽
Vol 39
(4)
◽
pp. 864-882
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Keyword(s):
Generalized local mean normal measures μz, z ∈ Rd, are introduced for a nonstationary process X of convex particles. For processes with strictly convex particles it is then shown that X is weakly stationary and weakly isotropic if and only if μz is rotation invariant for all z ∈ Rd. The paper is concluded by extending this result to processes of cylinders, generalizing Theorem 1 of Schneider (2003).
Keyword(s):
1963 ◽
Vol 106
(2)
◽
pp. 270-270
◽
2020 ◽
Vol 52
(1)
◽
pp. 471-480
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1999 ◽
Vol 19
(1)
◽
pp. 201-226
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2008 ◽
Vol 23
(2)
◽
pp. 241-250
2015 ◽
Vol 143
(9)
◽
pp. 3879-3893
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