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Volumn 36, Issue 6, 2008, Pages 2159-2175

Asymptotic behavior of weighted quadratic and cubic variations of fractional brownian motion

Author keywords

Breuer and major theorem; Exact rate of convergence; Fractional Brownian motion; Malliavin calculus; Weighted cubic variation; Weighted quadratic variation

Indexed keywords


EID: 48849108688     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/07-AOP385     Document Type: Article
Times cited : (59)

References (16)
  • 1
    • 0000323474 scopus 로고    scopus 로고
    • BREUER, P. and MAJOR, P. (1983). Central limit theorems for nonlinear functionals of Gaussian fields. J. Multivariate Anal. 13 425-441. MR716933
    • BREUER, P. and MAJOR, P. (1983). Central limit theorems for nonlinear functionals of Gaussian fields. J. Multivariate Anal. 13 425-441. MR716933
  • 2
    • 33845455397 scopus 로고    scopus 로고
    • Power variation of some integral fractional processes
    • MR2248234
    • CORCUERA, J. M., NUALART, D. and WOERNER, J. H. C. (2006). Power variation of some integral fractional processes. Bernoulli 12 713-735. MR2248234
    • (2006) Bernoulli , vol.12 , pp. 713-735
    • CORCUERA, J.M.1    NUALART, D.2    WOERNER, J.H.C.3
  • 3
    • 13844294706 scopus 로고    scopus 로고
    • DOBRUSHIN, R. L. and MAJOR, P. (1979). Non-central limit theorems for nonlinear functionals of Gaussian fields. Z. Wahrsch. Verw. Gebiete 50 27-52. MR550122
    • DOBRUSHIN, R. L. and MAJOR, P. (1979). Non-central limit theorems for nonlinear functionals of Gaussian fields. Z. Wahrsch. Verw. Gebiete 50 27-52. MR550122
  • 4
    • 51249172022 scopus 로고    scopus 로고
    • GIRAITIS, L. and SURGAILIS, D. (1985). CLT and other limit theorems for functionals of Gaussian processes. Z. Wahrsch. Verw. Gebiete 70 191-212. MR799146
    • GIRAITIS, L. and SURGAILIS, D. (1985). CLT and other limit theorems for functionals of Gaussian processes. Z. Wahrsch. Verw. Gebiete 70 191-212. MR799146
  • 5
    • 58549112098 scopus 로고    scopus 로고
    • Weighted power variations of fractional Brownian motion and application to approximating schemes
    • Preprint
    • GRADINARU, M. and NOURDIN, I. (2007). Weighted power variations of fractional Brownian motion and application to approximating schemes. Preprint.
    • (2007)
    • GRADINARU, M.1    NOURDIN, I.2
  • 6
    • 0346332490 scopus 로고    scopus 로고
    • GRADINARU, M., RUSSO, F. and VALLOIS, P. (2003). Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H Ann. Probab. 31 1772-1820. MR2016600
    • GRADINARU, M., RUSSO, F. and VALLOIS, P. (2003). Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H Ann. Probab. 31 1772-1820. MR2016600
  • 7
    • 61949339857 scopus 로고    scopus 로고
    • JACOD, J. (1994). Limit of random measures associated with the increments of a Brownian semimartingale. Preprint (revised version, unpublished manuscript).
    • JACOD, J. (1994). Limit of random measures associated with the increments of a Brownian semimartingale. Preprint (revised version, unpublished manuscript).
  • 8
    • 61949227453 scopus 로고    scopus 로고
    • KHOSHNEVISAN, D. and LEWIS, T. M. (1999). Iterated Brownian motion and its intrinsic skeletal structure. In Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1996). Progr. Probab. 45 201-210. Birkhäuser, Basel. MR 1712242
    • KHOSHNEVISAN, D. and LEWIS, T. M. (1999). Iterated Brownian motion and its intrinsic skeletal structure. In Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1996). Progr. Probab. 45 201-210. Birkhäuser, Basel. MR 1712242
  • 9
    • 33846550201 scopus 로고    scopus 로고
    • Limits for weighted p-variations and likewise functionals of fractional diffusions with drift
    • MR2290877
    • LEÖN, J. and LUDEÑ;A, C. (2007). Limits for weighted p-variations and likewise functionals of fractional diffusions with drift. Stochastic Process. Appl. 117 271-296. MR2290877
    • (2007) Stochastic Process. Appl , vol.117 , pp. 271-296
    • LEÖN, J.1    LUDEÑA, C.2
  • 10
    • 35548963865 scopus 로고    scopus 로고
    • Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion
    • MR2359060
    • NEUENKIRCH, A. and NOURDIN, I. (2007). Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion. J. Theoret. Probab. 20 871-899. MR2359060
    • (2007) J. Theoret. Probab , vol.20 , pp. 871-899
    • NEUENKIRCH, A.1    NOURDIN, I.2
  • 11
    • 61949234248 scopus 로고    scopus 로고
    • A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension one. Sém Probab
    • To appear
    • NOURDIN, I. (2007). A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension one. Sém Probab, XLI. To appear.
    • (2007) XLI
    • NOURDIN, I.1
  • 12
    • 53349178602 scopus 로고    scopus 로고
    • Central and non-central limit theorems for weighted power variations of fractional Brownian motion
    • Preprint
    • NOURDIN, I., NUALART, D. and TUDOR, C. A. (2007). Central and non-central limit theorems for weighted power variations of fractional Brownian motion. Preprint.
    • (2007)
    • NOURDIN, I.1    NUALART, D.2    TUDOR, C.A.3
  • 13
    • 48849095030 scopus 로고    scopus 로고
    • Weighted power variations of iterated Brownian motion
    • NOURDIN, I. and PECCATI, G. (2008). Weighted power variations of iterated Brownian motion. Electron. J. Probab. 13 1229-1256.
    • (2008) Electron. J. Probab , vol.13 , pp. 1229-1256
    • NOURDIN, I.1    PECCATI, G.2
  • 14
    • 61949328254 scopus 로고    scopus 로고
    • NUALART, D. (2003). Stochastic integration with respect to fractional Brownian motion and applications. In Stochastic Models {Mexico City, 2002). Contemp. Math. 336 3-39. Amer. Math. Soc, Providence, RI. MR2037156
    • NUALART, D. (2003). Stochastic integration with respect to fractional Brownian motion and applications. In Stochastic Models {Mexico City, 2002). Contemp. Math. 336 3-39. Amer. Math. Soc, Providence, RI. MR2037156
  • 15
    • 48849113065 scopus 로고    scopus 로고
    • Variations of the solution to a stochastic heat equation
    • MR2353385
    • SWANSON, J. (2007). Variations of the solution to a stochastic heat equation. Ann. Probab. 35 2122-2159. MR2353385
    • (2007) Ann. Probab , vol.35 , pp. 2122-2159
    • SWANSON, J.1
  • 16
    • 0001915941 scopus 로고    scopus 로고
    • TAQQU, M. S. (1979). Convergence of integrated processes of arbitrary Hermite rank. Z. Wahrsch. Verw. Gebiete 50 53-83. MR550123
    • TAQQU, M. S. (1979). Convergence of integrated processes of arbitrary Hermite rank. Z. Wahrsch. Verw. Gebiete 50 53-83. MR550123


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