Open Access
May, 1984 On the Cadlaguity of Random Measures
Robert J. Adler, Paul D. Feigin
Ann. Probab. 12(2): 615-630 (May, 1984). DOI: 10.1214/aop/1176993309


We consider finitely additive random measures taking independent values on disjoint Borel sets in $R^k$, and ask when such measures, restricted to some subclass $\mathscr{A}$ of closed Borel sets, possess versions which are "right continuous with left limits", in an appropriate sense. The answer involves a delicate relationship between the "Levy measure" of the random measure and the size of $\mathscr{A}$, as measured via an entropy condition. Examples involving stable measures, Dudley's class $I(k, \alpha, M)$ of sets in $R^k$ with $\alpha$-times differentiable boundaries, and convex sets are considered as special cases, and an example given to show what can go wrong when the entropy of $\mathscr{A}$ is too large.


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Robert J. Adler. Paul D. Feigin. "On the Cadlaguity of Random Measures." Ann. Probab. 12 (2) 615 - 630, May, 1984.


Published: May, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0542.60050
MathSciNet: MR735857
Digital Object Identifier: 10.1214/aop/1176993309

Primary: 60G17
Secondary: 60G15 , 60J30

Keywords: cadlag , convex sets , Entropy , Independent increments , Random measures

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 2 • May, 1984
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