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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Multiple points of a random field


Author: Narn Rueih Shieh
Journal: Proc. Amer. Math. Soc. 92 (1984), 279-282
MSC: Primary 60G17; Secondary 60G15, 60G60
DOI: https://doi.org/10.1090/S0002-9939-1984-0754721-2
MathSciNet review: 754721
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Abstract: We prove that a $ d$-dimensional random field $ X \equiv {\{ X(t)\} _{t \in R_ + ^N}}$ has uncountably many $ r$-multiple points a.s. when it satisfies Pitt's ($ ({A_r})$) condition [9]. Those $ t$'s for which $ X(t)$ hits the multiple point can be separated by any given positive number, and multiple points can occur while $ t$ is restricted to any given "time inteval". Two corollaries concerning Gaussian fields and fields with independent increments are also presented.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0754721-2
Keywords: Multiple points, local times, random fields, Pitt's condition
Article copyright: © Copyright 1984 American Mathematical Society