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Limit theorems for the square integral of Brownian motion and its increments

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  • Li, Wenbo V.

Abstract

Strassen's functional law of the iterated logarithm can be used to prove limit results about Brownian motion, but the limiting constants are given implicitly in many cases. In this paper, we provide a probabilistic method that can give the limiting constants explicitly for the square integral of Brownian motion and its increments.

Suggested Citation

  • Li, Wenbo V., 1992. "Limit theorems for the square integral of Brownian motion and its increments," Stochastic Processes and their Applications, Elsevier, vol. 41(2), pages 223-239, June.
    • Handle: RePEc:eee:spapps:v:41:y:1992:i:2:p:223-239
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    Citations

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    Cited by:

    1. Ai, Xiaohui & Li, Wenbo V. & Liu, Guoqing, 2012. "Karhunen–Loeve expansions for the detrended Brownian motion," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1235-1241.
    2. Kung-Sik Chan & Simone Giannerini & Greta Goracci & Howell Tong, 2020. "Testing for threshold regulation in presence of measurement error with an application to the PPP hypothesis," Papers 2002.09968, arXiv.org, revised Nov 2021.
    3. Albin, J. M. P., 1995. "Upper and lower classes for 2 - and p-norms of Brownian motion and norms of [alpha]-stable motion," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 91-103, July.
    4. Wang, Xudong & Chen, Yao, 2021. "Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    5. Deheuvels, Paul, 2007. "A Karhunen-Loeve expansion for a mean-centered Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1190-1200, July.
    6. Wang, Zhenhai & Wang, Xudong, 2024. "Landscapes of random diffusivity processes in harmonic potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).

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