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December 2015 Estimation of integrals with respect to infinite measures using regenerative sequences
Krishna B. Athreya, Vivekananda Roy
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J. Appl. Probab. 52(4): 1133-1145 (December 2015). DOI: 10.1239/jap/1450802757

Abstract

Let f be an integrable function on an infinite measure space(S, S, π). We show that if a regenerativesequence {Xn}n≥0 withcanonical measure π could be generated then a consistent estimator ofλ ≡ ∫Sfdπ can be produced.We further show that under appropriate second moment conditions, a confidenceinterval for λ can also be derived. This is illustrated with estimatingcountable sums and integrals with respect to absolutely continuous measures onRd using a simple symmetric random walk on Z.

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Krishna B. Athreya. Vivekananda Roy. "Estimation of integrals with respect to infinite measures using regenerative sequences." J. Appl. Probab. 52 (4) 1133 - 1145, December 2015. https://doi.org/10.1239/jap/1450802757

Information

Published: December 2015
First available in Project Euclid: 22 December 2015

zbMATH: 1334.65003
MathSciNet: MR3439176
Digital Object Identifier: 10.1239/jap/1450802757

Subjects:
Primary: 65C05
Secondary: 60F05

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 4 • December 2015
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