Communications for Statistical Applications and Methods

  • 제18권6호
  • /
  • Pages.851-857
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  • 2011
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Central Limit Theorem of the Cross Variation Related to Fractional Brownian Sheet

  • 투고 : 20110500
  • 심사 : 20110900
  • 발행 : 2011.11.30
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초록

By using Malliavin calculus, we study a central limit theorem of the cross variation related to fractional Brownian sheet with Hurst parameter H = ($H_1$, $H_2$) such that 1/4 < $H_1$ < 1/2 and 1/4 < $H_2$ < 1/2.

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참고문헌

  1. Kim, Y. T., Jeon, J. W. and Park, H. S. (2008). Various types of stochastic integrals with respect to fractional Brownian sheet and their applications, Journal of Mathematical Analysis and Applications, 341, 1382-1398. https://doi.org/10.1016/j.jmaa.2007.10.071
  2. Nourdin, I. (2008). Asymptotic behavior of certain weighted quadratic and cubic variations of fractional Brownian motion, The Annals of Probability, 36, 2159-2175. https://doi.org/10.1214/07-AOP385
  3. Nourdin, I. and Nualart, D. (2008). Central limit theorems for multiple Skorohod integrals, Preprint.
  4. Nourdin, I., Nualart, D. and Tudor, C. A. (2010). Central and non-central limit theorems for weighted power variations of fractional Brownian motion, Annales de l'Institut Henri Poincare-Probabilites et Statistiques, 46, 1055-1079. https://doi.org/10.1214/09-AIHP342
  5. Nualart, D. (2006). Malliavin Calculus and Related Topics, 2nd Ed., Springer.
  6. Nualart, D. and Ortiz-Latorre, S. (2008). Central limit theorems for multiple stochastic integrals and Malliavin calculus, Stochastic Processes and their Applications, 118, 614-628. https://doi.org/10.1016/j.spa.2007.05.004
  7. Nualart, D. and Peccati, G. (2005). Central limit theorems for sequences of multiple stochastic integrals, The Annals of Probability, 33, 173-193.
  8. Park, H. S., Jeon, J. W. and Kim, Y. T. (2011). The central limit theorem for cross-variation related to the standard Brownian sheet and Berry-Essen bounds, Journal of the Korean Statistical Society, 40, 239-244. https://doi.org/10.1016/j.jkss.2010.10.002
  9. Reveillac, A. (2009a), Estimation of quadratic variation for two-parameter diffusions, Stochastic Processes and their Applications, 119, 1652-1672. https://doi.org/10.1016/j.spa.2008.08.006
  10. Reveillac, A. (2009b). Convergence of finite-dimensional laws of the weighted quadratic variation for some fractional Brownian sheet, Stochastic Analaysis and its Applications, 27, 51-73. https://doi.org/10.1080/07362990802564491

피인용 문헌

  1. Asymptotic Behavior of the Weighted Cross-Variation of a Fractional Brownian Sheet vol.19, pp.3, 2012, https://doi.org/10.5351/CKSS.2012.19.3.303
  2. Berry-Esséen bounds and almost sure CLT for quadratic variation of weighted fractional Brownian motion vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-275