@article{AIHPB_2005__41_4_781_0, author = {Gradinaru, Mihai and Nourdin, Ivan and Russo, Francesco and Vallois, Pierre}, title = {$m$-order integrals and generalized {It\^o{\textquoteright}s} formula ; the case of a fractional brownian motion with any {Hurst} index}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {781--806}, publisher = {Elsevier}, volume = {41}, number = {4}, year = {2005}, doi = {10.1016/j.anihpb.2004.06.002}, zbl = {1083.60045}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2004.06.002/} }
TY - JOUR AU - Gradinaru, Mihai AU - Nourdin, Ivan AU - Russo, Francesco AU - Vallois, Pierre TI - $m$-order integrals and generalized Itô’s formula ; the case of a fractional brownian motion with any Hurst index JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2005 SP - 781 EP - 806 VL - 41 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpb.2004.06.002/ DO - 10.1016/j.anihpb.2004.06.002 LA - en ID - AIHPB_2005__41_4_781_0 ER -
%0 Journal Article %A Gradinaru, Mihai %A Nourdin, Ivan %A Russo, Francesco %A Vallois, Pierre %T $m$-order integrals and generalized Itô’s formula ; the case of a fractional brownian motion with any Hurst index %J Annales de l'I.H.P. Probabilités et statistiques %D 2005 %P 781-806 %V 41 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpb.2004.06.002/ %R 10.1016/j.anihpb.2004.06.002 %G en %F AIHPB_2005__41_4_781_0
Gradinaru, Mihai; Nourdin, Ivan; Russo, Francesco; Vallois, Pierre. $m$-order integrals and generalized Itô’s formula ; the case of a fractional brownian motion with any Hurst index. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 4, pp. 781-806. doi : 10.1016/j.anihpb.2004.06.002. http://archive.numdam.org/articles/10.1016/j.anihpb.2004.06.002/
[1] Stratonovich calculus for fractional Brownian motion with Hurst parameter less than , Taiwanese J. Math. 5 (2001) 609-632. | MR | Zbl
, , ,[2] An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter, Stochastic Process. Appl. 124 (1) (2003) 81-106. | MR | Zbl
,[3] Stochastic integration with respect to fractional Brownian motion, Ann. Inst. H. Poincaré Probab. Statist. 39 (1) (2003) 27-68. | Numdam | MR | Zbl
, , ,[4] P. Cheridito, D. Nualart, Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter , Preprint, Barcelona, 2002.
[5] Stochastic analysis, rough path analysis and fractional Brownian motions, Probab. Theory Related Fields 122 (1) (2002) 108-140. | MR | Zbl
, ,[6] Stochastic analysis of the fractional Brownian motion, Potential Anal. 10 (1998) 177-214. | MR | Zbl
, ,[7] Differentiability of Six Operators on Nonsmooth Functions and p-variation, Lecture Notes in Math., vol. 1703, Springer-Verlag, 1999. | MR | Zbl
, ,[8] Covariation de convolutions de martingales, C. R. Acad. Sci. Sér. 1 326 (1998) 601-609. | MR | Zbl
, ,[9] n-covariation and symmetric SDEs driven by finite cubic variation process, Stoch. Process. Appl. 104 (2) (2000) 259-299. | MR | Zbl
, ,[10] On fractional Brownian processes, Potential Anal. 10 (3) (1999) 273-288. | MR | Zbl
, ,[11] Calcul d'Itô sans probabilités, in: Séminaire de Probabilités XV 1979/80, Lecture Notes in Math., vol. 850, Springer-Verlag, 1981, pp. 143-150. | Numdam | MR | Zbl
,[12] Quadratic covariation and an extension of Itô's formula, Bernoulli 1 (1995) 149-169. | MR | Zbl
, , ,[13] Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, 1994. | MR | Zbl
, ,[14] Approximation at first and second order of the m-variation of the fractional Brownian motion, Electron. J. Probab. 8 (2003) 1-26, Paper 18. | MR | Zbl
, ,[15] Generalized covariations, local time and Stratonovich Itô’s formula for fractional Brownian motion with Hurst index , Ann. Probab. 31 (2003) 1772-1820. | Zbl
, , ,[16] Differential equations driven by rough signals, Rev. Mat. Iberoamericana 14 (2) (1998) 215-310. | MR | Zbl
,[17] A crossing estimate for the canonical process on a Dirichlet space and tightness result, Astérisque 157-158 (1998) 249-271. | Numdam | MR | Zbl
, ,[18] Stochastic calculus for continuous additive functionals of zero energy, Wahrs. Verw. Geb. 68 (1995) 557-578, (1985). | MR | Zbl
,[19] I. Nourdin, PhD Thesis, Nancy, 2004.
[20] The Malliavin Calculus and Related Topics, Springer-Verlag, 1995. | MR | Zbl
,[21] Skorohod and pathwise stochastic calculus with respect to a - process, Random Operators and Stochastic Equations 8 (3) (2000) 1-24. | MR | Zbl
, ,[22] The generalized covariation process and Itô formula, Stochastic Process. Appl. 59 (1995) 81-104. | MR | Zbl
, ,[23] Itô formula for -functions of semimartingales, Probab. Theory Related. Fields 104 (1996) 27-41. | MR | Zbl
, ,[24] Stochastic calculus with respect to a finite quadratic variation process, Stochastics and Stochastics Reports 70 (2000) 1-40. | MR | Zbl
, ,[25] Introduction to Numerical Analysis, Springer-Verlag, 1983. | Zbl
, , , , ,[26] Stochastic calculus of generalized Dirichlet forms and applications to stochastic differential equations in infinite dimensions, Osaka J. Math. 37 (2) (2000) 315-343. | MR | Zbl
,[27] An Itô Formula for local Dirichlet processes, Stochastics and Stochastics Reports 62 (2) (1997) 103-115. | MR | Zbl
,[28] Sur quelques approximations d'intégrales stochastiques, in: Séminaire de Probabilités XI 1975/76, Lecture Notes in Math., vol. 581, Springer-Verlag, 1975, pp. 518-528. | Numdam | MR | Zbl
,[29] Integration with respect to fractal functions and stochastic calculus I, Probab. Theory Related Fields 111 (1998) 333-374. | MR | Zbl
,Cité par Sources :