Athreya, Krishna B. ; Normand, Raoul ; Roy, Vivekananda ; Wu, Sheng-Jhih (2015) Limit theorems for the estimation of L1 integrals using the Brownian motion Statistics & Probability Letters, 100 . pp. 42-47. ISSN 01677152
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Official URL: http://doi.org/10.1016/j.spl.2015.01.034
Related URL: http://dx.doi.org/10.1016/j.spl.2015.01.034
Abstract
We provide a point estimate for integrals on , 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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier B.V. |
| Keywords: | Brownian motion, Local time, Point estimate, Ray–Knight theorem, Regenerative process |
| ID Code: | 131563 |
| Deposited On: | 07 Dec 2022 06:16 |
| Last Modified: | 07 Dec 2022 06:16 |
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