Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter H∈(0,1 2)
Cheridito, Patrick ; Nualart, David
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005), p. 1049-1081 / Harvested from Numdam
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@article{AIHPB_2005__41_6_1049_0,
     author = {Cheridito, Patrick and Nualart, David},
     title = {Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter $H\in (0,\frac{1}{2})$},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {41},
     year = {2005},
     pages = {1049-1081},
     doi = {10.1016/j.anihpb.2004.09.004},
     mrnumber = {2172209},
     zbl = {1083.60027},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2005__41_6_1049_0}
}

Cheridito, Patrick; Nualart, David. Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter $H\in (0,\frac{1}{2})$. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) pp. 1049-1081. doi : 10.1016/j.anihpb.2004.09.004. http://gdmltest.u-ga.fr/item/AIHPB_2005__41_6_1049_0/

[1] 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. | MR 1849782 | Zbl 0989.60054

[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. | MR 1741199 | Zbl 1028.60047

[3] E. Alòs, O. Mazet, D. Nualart, Stochastic calculus with respect to Gaussian processes, Ann. Probab. 29 (2) (2001) 766-801. | MR 1849177 | Zbl 1015.60047

[4] 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. | MR 1956473 | Zbl 1075.60530

[5] S. Berman, Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J. 23 (1973) 69-94. | MR 317397 | Zbl 0264.60024

[6] P. Carmona, L. Coutin, G. Montseny, Stochastic integration with respect to fractional Brownian motion, Ann. Inst. H. Poincaré Probab. Statist. 39 (1) (2003) 27-68. | Numdam | MR 1959841 | Zbl 1016.60043

[7] L. Coutin, D. Nualart, C.A. Tudor, Tanaka formula for the fractional Brownian motion, Stochastic Process Appl. 94 (2) (2001) 301-315. | MR 1840834 | Zbl 1053.60055

[8] L. Coutin, Z. Qian, Stochastic analysis, rough path analysis and fractional Brownian motions, Probab. Theory Related Fields 122 (1) (2002) 108-140. | MR 1883719 | Zbl 1047.60029

[9] L. Decreusefond, A.S. Üstünel, Stochastic analysis of the fractional Brownian motion, Potential Anal. 10 (2) (1999) 177-214. | MR 1677455 | Zbl 0924.60034

[10] 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. | MR 1741154 | Zbl 0947.60061

[11] B. Gaveau, P. Trauber, L'integrale stochastique comme opérateur de divergence dans l'espace fonctionnel, J. Funct. Anal. 46 (2) (1982) 230-238. | MR 660187 | Zbl 0488.60068

[12] 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. | Zbl 1059.60067

[13] 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.

[14] Y. Hu, Probability structure preserving and absolute continuity, Ann. Inst. H. Poincaré 38 (4) (2002) 557-580. | Numdam | MR 1914939 | Zbl 1002.60046

[15] Y. Hu, B. Øksendal, Fractional white noise calculus and applications to finance, Inf. Dim. Anal. Quant. Probab. Rel. Top. 6 (1) (2003) 1-32. | MR 1976868 | Zbl 1045.60072

[16] K. Itô, Stochastic integral, Proc. Imperial Acad. Tokyo 20 (1944) 519-524. | MR 14633 | Zbl 0060.29105

[17] S.J. Lin, Stochastic analysis of fractional Brownian motions, Stochastics Stochastics Rep. 55 (1995) 121-140. | MR 1382288 | Zbl 0886.60076

[18] Sh.R. Liptser, A.N. Shiryaev, Theory of Martingales, Kluwer Academic, Dordrecht, 1989. | MR 1022664 | Zbl 0728.60048

[19] S. Maheswaran, C.A. Sims, Empirical implications of arbitrage-free asset markets, in: Phillips P.C.B. (Ed.), Models, Methods and Applications of Econometrics, Blackwell, 1993.

[20] P. Malliavin, Stochastic Analysis, Springer, 1997. | MR 1450093 | Zbl 0878.60001

[21] T. Mikosch, R. Norvaiša, Stochastic integral equations without probability, Bernoulli 6 (3) (2000) 401-434. | MR 1762553 | Zbl 0963.60060

[22] D. Nualart, The Malliavin Calculus and Related Topics, Springer, 1995. | MR 1344217 | Zbl 0837.60050

[23] D. Nualart, E. Pardoux, Stochastic calculus with anticipating integrands, Probab. Theory Related Fields 78 (4) (1988) 535-581. | MR 950346 | Zbl 0629.60061

[24] V. Pipiras, M.S. Taqqu, Integration questions related to fractional Brownian motion, Probab. Theory Related Fields 118 (2) (2000) 251-291. | MR 1790083 | Zbl 0970.60058

[25] V. Pipiras, M.S. Taqqu, Are classes of deterministic integrands for fractional Brownian motion on an interval complete?, Bernoulli 7 (6) (2001) 873-897. | MR 1873833 | Zbl 1003.60055

[26] N. Privault, Skorohod stochastic integration with respect to non-adapted processes on Wiener space, Stochastics Stochastics Rep. 65 (1998) 13-39. | MR 1708428 | Zbl 0918.60038

[27] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, 1999. | MR 1725357 | Zbl 0917.60006

[28] F. Russo, P. Vallois, Forward, backward and symmetric stochastic integration, Probab. Theory Related Fields 97 (3) (1993) 403-421. | MR 1245252 | Zbl 0792.60046

[29] F. Russo, P. Vallois, The generalized covariation process and Itô formula, Stochastic Process Appl. 59 (1) (1995) 81-104. | MR 1350257 | Zbl 0840.60052

[30] F. Russo, P. Vallois, Itô formula for C 1 -functions of semimartingales, Probab. Theory Related Fields 104 (1) (1996) 27-41. | MR 1367665 | Zbl 0838.60045

[31] L.C.G. Rogers, Arbitrage with fractional Brownian motion, Math. Finance 7 (1) (1997) 95-105. | MR 1434408 | Zbl 0884.90045

[32] F.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach, 1993. | MR 1347689 | Zbl 0818.26003

[33] L.C. Young, An inequality of the Hölder type, connected with Stieltjes integration, Acta Math. (Sweden) 67 (1936) 251-282. | MR 1555421 | Zbl 0016.10404

[34] M. Zähle, Integration with respect to fractal functions and stochasic calculus. I, Probab. Theory Related Fields 111 (3) (1998) 333-374. | MR 1640795 | Zbl 0918.60037