Integrability of infinite weighted sums of heavy-tailed i.i.d. random variables

Martin P. W. Zerner

Stochastic Processes and their Applications, 2002, vol. 99, issue 1, 81-94

Abstract: We consider the sum X of i.i.d. random variables Yn, n[greater-or-equal, slanted]0, with weights an which decay exponentially fast to zero. For a smooth sublinear increasing function g, g(Y0) has finite expectation if and only if the expectation of Xg'(X) is finite. The proof uses characteristic functions. However, if g grows polynomially or exponentially fast, then the expectation of g(Y0) is finite if and only if the expectation of g(X) is finite.

Keywords: Characteristic; function; Heavy; tail; Integrability; Linear; process; Stationary; distribution; Sum; of; independent; random; variables (search for similar items in EconPapers)
Date: 2002
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