메뉴 건너뛰기




Volumn 41, Issue 6, 2005, Pages 1049-1081

Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H ∈ (0, 1/2)

Author keywords

Fractional Brownian motion; Malliavin calculus; Stochastic integration; Symmetric integral

Indexed keywords


EID: 26844554101     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpb.2004.09.004     Document Type: Article
Times cited : (99)

References (34)
  • 1
    • 0038433460 scopus 로고    scopus 로고
    • Stochastic Stratonovich calculus for fractional Brownian motion with Hurst parameter less than 1/2
    • E. Alòs J.A. León D. Nualart Stochastic Stratonovich calculus for fractional Brownian motion with Hurst parameter less than 1/ 2 Taiwanese J. Math. 5 3 2001 609-632
    • (2001) Taiwanese J. Math. , vol.5 , Issue.3 , pp. 609-632
    • Alòs, E.1    León, J.A.2    Nualart, D.3
  • 2
    • 0000338690 scopus 로고    scopus 로고
    • Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 1/2
    • E. Alòs O. Mazet D. Nualart Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 1/2 Stochastic Process Appl. 86 1 2000 121-139
    • (2000) Stochastic Process Appl. , vol.86 , Issue.1 , pp. 121-139
    • Alòs, E.1    Mazet, O.2    Nualart, D.3
  • 3
    • 0035537291 scopus 로고    scopus 로고
    • Stochastic calculus with respect to Gaussian processes
    • E. Alòs O. Mazet D. Nualart Stochastic calculus with respect to Gaussian processes Ann. Probab. 29 2 2001 766-801
    • (2001) Ann. Probab. , vol.29 , Issue.2 , pp. 766-801
    • Alòs, E.1    Mazet, O.2    Nualart, D.3
  • 4
    • 0037361234 scopus 로고    scopus 로고
    • An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter
    • C. Bender An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter Stochastic Process Appl. 104 1 2003 81-106
    • (2003) Stochastic Process Appl. , vol.104 , Issue.1 , pp. 81-106
    • Bender, C.1
  • 5
    • 0002807832 scopus 로고
    • Local nondeterminism and local times of Gaussian processes
    • S. Berman Local nondeterminism and local times of Gaussian processes Indiana Univ. Math. J. 23 1973 69-94
    • (1973) Indiana Univ. Math. J. , vol.23 , pp. 69-94
    • Berman, S.1
  • 7
    • 0042909263 scopus 로고    scopus 로고
    • Tanaka formula for the fractional Brownian motion
    • L. Coutin D. Nualart C.A. Tudor Tanaka formula for the fractional Brownian motion Stochastic Process Appl. 94 2 2001 301-315
    • (2001) Stochastic Process Appl. , vol.94 , Issue.2 , pp. 301-315
    • Coutin, L.1    Nualart, D.2    Tudor, C.A.3
  • 8
    • 0036002985 scopus 로고    scopus 로고
    • Stochastic analysis, rough path analysis and fractional Brownian motions
    • L. Coutin Z. Qian Stochastic analysis, rough path analysis and fractional Brownian motions Probab. Theory Related Fields 122 1 2002 108-140
    • (2002) Probab. Theory Related Fields , vol.122 , Issue.1 , pp. 108-140
    • Coutin, L.1    Qian, Z.2
  • 9
    • 0042637937 scopus 로고    scopus 로고
    • Stochastic analysis of the fractional Brownian motion
    • L. Decreusefond A.S. Üstünel Stochastic analysis of the fractional Brownian motion Potential Anal. 10 2 1999 177-214
    • (1999) Potential Anal. , vol.10 , Issue.2 , pp. 177-214
    • Decreusefond, L.1    Üstünel, A.S.2
  • 10
    • 0033878593 scopus 로고    scopus 로고
    • Stochastic calculus for fractional Brownian motion I. Theory
    • T.E. Duncan Y. Hu B. Pasik-Duncan Stochastic calculus for fractional Brownian motion I. Theory SIAM J. Control Optim. 38 2 2000 582-612
    • (2000) SIAM J. Control Optim. , vol.38 , Issue.2 , pp. 582-612
    • Duncan, T.E.1    Hu, Y.2    Pasik-Duncan, B.3
  • 11
    • 0001134054 scopus 로고
    • L'integrale stochastique comme opérateur de divergence dans l'espace fonctionnel
    • B. Gaveau P. Trauber L'integrale stochastique comme opérateur de divergence dans l'espace fonctionnel J. Funct. Anal. 46 2 1982 230-238
    • (1982) J. Funct. Anal. , vol.46 , Issue.2 , pp. 230-238
    • Gaveau, B.1    Trauber, P.2
  • 12
    • 0346332490 scopus 로고    scopus 로고
    • Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H≥1/4
    • M. Gradinaru F. Russo P. Vallois Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H ≥ 1/4 Ann. Probab. 31 4 2003 1772-1820
    • (2003) Ann. Probab. , vol.31 , Issue.4 , pp. 1772-1820
    • Gradinaru, M.1    Russo, F.2    Vallois, P.3
  • 13
    • 18144363052 scopus 로고    scopus 로고
    • m-order integrals and generalized Itô's formula: The case of a fractional Brownian motion with any Hurst index
    • Preprint
    • M. Gradinaru, I. Nourdin, F. Russo, P. Vallois, m-order integrals and generalized Itô's formula: The case of a fractional Brownian motion with any Hurst index, Preprint, 2002
    • (2002)
    • Gradinaru, M.1    Nourdin, I.2    Russo, F.3    Vallois, P.4
  • 14
    • 0036267644 scopus 로고    scopus 로고
    • Probability structure preserving and absolute continuity
    • Y. Hu Probability structure preserving and absolute continuity Ann. Inst. H. Poincaré 38 4 2002 557-580
    • (2002) Ann. Inst. H. Poincaré , vol.38 , Issue.4 , pp. 557-580
    • Hu, Y.1
  • 15
    • 0038246338 scopus 로고    scopus 로고
    • Fractional white noise calculus and applications to finance
    • Y. Hu B. Øksendal Fractional white noise calculus and applications to finance Inf. Dim. Anal. Quant. Probab. Rel. Top. 6 1 2003 1-32
    • (2003) Inf. Dim. Anal. Quant. Probab. Rel. Top. , vol.6 , Issue.1 , pp. 1-32
    • Hu, Y.1    Øksendal, B.2
  • 17
    • 0000746261 scopus 로고
    • Stochastic analysis of fractional Brownian motions
    • S.J. Lin Stochastic analysis of fractional Brownian motions Stochastics Stochastics Rep. 55 1995 121-140
    • (1995) Stochastics Stochastics Rep. , vol.55 , pp. 121-140
    • Lin, S.J.1
  • 21
    • 0013336217 scopus 로고    scopus 로고
    • Stochastic integral equations without probability
    • T. Mikosch R. Norvaiša Stochastic integral equations without probability Bernoulli 6 3 2000 401-434
    • (2000) Bernoulli , vol.6 , Issue.3 , pp. 401-434
    • Mikosch, T.1    Norvaiša, R.2
  • 23
    • 0001626619 scopus 로고
    • Stochastic calculus with anticipating integrands
    • D. Nualart E. Pardoux Stochastic calculus with anticipating integrands Probab. Theory Related Fields 78 4 1988 535-581
    • (1988) Probab. Theory Related Fields , vol.78 , Issue.4 , pp. 535-581
    • Nualart, D.1    Pardoux, E.2
  • 24
    • 0034562433 scopus 로고    scopus 로고
    • Integration questions related to fractional Brownian motion
    • V. Pipiras M.S. Taqqu Integration questions related to fractional Brownian motion Probab. Theory Related Fields 118 2 2000 251-291
    • (2000) Probab. Theory Related Fields , vol.118 , Issue.2 , pp. 251-291
    • Pipiras, V.1    Taqqu, M.S.2
  • 25
    • 33750073208 scopus 로고    scopus 로고
    • Are classes of deterministic integrands for fractional Brownian motion on an interval complete?
    • V. Pipiras M.S. Taqqu Are classes of deterministic integrands for fractional Brownian motion on an interval complete? Bernoulli 7 6 2001 873-897
    • (2001) Bernoulli , vol.7 , Issue.6 , pp. 873-897
    • Pipiras, V.1    Taqqu, M.S.2
  • 26
    • 0001900180 scopus 로고    scopus 로고
    • Skorohod stochastic integration with respect to non-adapted processes on Wiener space
    • N. Privault Skorohod stochastic integration with respect to non-adapted processes on Wiener space Stochastics Stochastics Rep. 65 1998 13-39
    • (1998) Stochastics Stochastics Rep. , vol.65 , pp. 13-39
    • Privault, N.1
  • 28
    • 21344479524 scopus 로고
    • Forward, backward and symmetric stochastic integration
    • F. Russo P. Vallois Forward, backward and symmetric stochastic integration Probab. Theory Related Fields 97 3 1993 403-421
    • (1993) Probab. Theory Related Fields , vol.97 , Issue.3 , pp. 403-421
    • Russo, F.1    Vallois, P.2
  • 29
    • 0001967383 scopus 로고
    • The generalized covariation process and Itô formula
    • F. Russo P. Vallois The generalized covariation process and Itô formula Stochastic Process Appl. 59 1 1995 81-104
    • (1995) Stochastic Process Appl. , vol.59 , Issue.1 , pp. 81-104
    • Russo, F.1    Vallois, P.2
  • 31
    • 0031540977 scopus 로고    scopus 로고
    • Arbitrage with fractional Brownian motion
    • L.C.G. Rogers Arbitrage with fractional Brownian motion Math. Finance 7 1 1997 95-105
    • (1997) Math. Finance , vol.7 , Issue.1 , pp. 95-105
    • Rogers, L.C.G.1
  • 33
    • 0000821514 scopus 로고
    • An inequality of the Hölder type, connected with Stieltjes integration
    • L.C. Young An inequality of the Hölder type, connected with Stieltjes integration Acta Math. (Sweden) 67 1936 251-282
    • (1936) Acta Math. (Sweden) , vol.67 , pp. 251-282
    • Young, L.C.1
  • 34
    • 0038290919 scopus 로고    scopus 로고
    • Integration with respect to fractal functions and stochasic calculus
    • M. Zähle Integration with respect to fractal functions and stochasic calculus. I Probab. Theory Related Fields 111 3 1998 333-374
    • (1998) I, Probab. Theory Related Fields , vol.111 , Issue.3 , pp. 333-374
    • Zähle, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.