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Moderate deviation principle for Brownian motions on the unit sphere in Rd

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  • Chen, Lei
  • Gao, Fuqing

Abstract

In this paper, we obtain the moderate deviation principle for a sequence of Brownian motions defined on the unit sphere in Rd by using the cumulant method introduced by Puhalskii (1994b) and generalize it to Ornstein–Uhlenbeck processes taking values on the unit sphere in Rd.

Suggested Citation

  • Chen, Lei & Gao, Fuqing, 2013. "Moderate deviation principle for Brownian motions on the unit sphere in Rd," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2486-2491.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:11:p:2486-2491
    DOI: 10.1016/j.spl.2013.07.010
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    References listed on IDEAS

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    1. Puhalskii, A., 1994. "The method of stochastic exponentials for large deviations," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 45-70, November.
    2. Gao, Fu-Qing, 1996. "Moderate deviations for martingales and mixing random processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 263-275, February.
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