Some Linear Random Functionals Characterized by L p -Symmetries

Olav Kallenberg
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Olav Kallenberg: Auburn University, Departments of Mathematics

A chapter in Stochastic Processes, 1993, pp 171-180 from Springer

Abstract: Abstract Consider a linear random functional ξ on some real or complex linear space L, along with a linear operator A from L into a space L p (S, μ). Under suitable regularity conditions, it is shown that if P(ξf) −1 depends only on ∥Af ∥ P , then ξ must be of the form σ ∫ Af dX, where X denotes symmetric p-stable noise on S with control measure μ, while σ ≥ 0 is an independent r.v. The result generalizes Schoenberg’s classical theorem and has many interesting applications.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-7909-0_20

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DOI: 10.1007/978-1-4615-7909-0_20

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