Uncorrelatedness sets for random variables with given distributions

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2005

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Amer Mathematical Soc

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Mathematics
(2000)
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Abstract

Let xi(1) and xi(2) be random variables having finite moments of all orders. The set U(xi(1),xi(2)) := {( j, l) is an element of N-2 : E(xi(1)(j)xi(2)(l)) = E(xi(1)(j)) E(xi(2)(l))} is said to be an uncorrelatedness set of xi(1) and xi(2). It is known that in general, an uncorrelatedness set can be arbitrary. Simple examples show that this is not true for random variables with given distributions. In this paper we present a wide class of probability distributions such that there exist random variables with given distributions from the class having a prescribed uncorrelatedness set. Besides, we discuss the sharpness of the obtained result.

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uncorrelatedness, independence, uncorrelatedness set, quasianalytic class, characteristic function

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4

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Volume

133

Issue

4

Start Page

1239

End Page

1246

URI

https://doi.org/10.1090/S0002-9939-04-07698-1
 https://hdl.handle.net/20.500.14411/1226

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