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Estimation of integrals with respect to infinite measures using regenerative sequences
- Part of
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- Journal:
- Journal of Applied Probability / Volume 52 / Issue 4 / December 2015
- Published online by Cambridge University Press:
- 30 March 2016, pp. 1133-1145
- Print publication:
- December 2015
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- Article
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Let f be an integrable function on an infinite measure space (S,
, π). We show that if a regenerative sequence {Xn}n≥0 with canonical measure π could be generated then a consistent estimator of λ ≡ ∫Sf dπ can be produced. We further show that under appropriate second moment conditions, a confidence interval for λ can also be derived. This is illustrated with estimating countable sums and integrals with respect to absolutely continuous measures on ℝd using a simple symmetric random walk on ℤ.
, π). We show that if a 