Limit theorems for the estimation of L1 integrals using the Brownian motion

Krishna B. Athreya, Raoul Normand, Vivekananda Roy and Sheng-Jhih Wu

Statistics & Probability Letters, 2015, vol. 100, issue C, 42-47

Abstract: We provide a point estimate for integrals on R, based on the standard Brownian motion. We prove the consistency of the estimator and limit theorems for the fluctuations. The proof relies on computing the distribution of the local time of a Brownian motion at a specific stopping time.

Keywords: Brownian motion; Local time; Point estimate; Ray–Knight theorem; Regenerative process (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.01.034

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