References
- 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
- 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
- Nourdin, I. and Nualart, D. (2008). Central limit theorems for multiple Skorohod integrals, Preprint.
- 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
- Nualart, D. (2006). Malliavin Calculus and Related Topics, 2nd Ed., Springer.
- 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
- Nualart, D. and Peccati, G. (2005). Central limit theorems for sequences of multiple stochastic integrals, The Annals of Probability, 33, 173-193.
- 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
- 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
- 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
Cited by
- 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
- 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