@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},
pages = {1049--1081},
year = {2005},
publisher = {Elsevier},
volume = {41},
number = {6},
doi = {10.1016/j.anihpb.2004.09.004},
mrnumber = {2172209},
zbl = {1083.60027},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpb.2004.09.004/}
}
TY - JOUR
AU - Cheridito, Patrick
AU - Nualart, David
TI - Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter $H\in (0,\frac{1}{2})$
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
SP - 1049
EP - 1081
VL - 41
IS - 6
PB - Elsevier
UR - https://www.numdam.org/articles/10.1016/j.anihpb.2004.09.004/
DO - 10.1016/j.anihpb.2004.09.004
LA - en
ID - AIHPB_2005__41_6_1049_0
ER -
%0 Journal Article
%A Cheridito, Patrick
%A Nualart, David
%T Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter $H\in (0,\frac{1}{2})$
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2005
%P 1049-1081
%V 41
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpb.2004.09.004/
%R 10.1016/j.anihpb.2004.09.004
%G en
%F 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) no. 6, pp. 1049-1081. doi: 10.1016/j.anihpb.2004.09.004
[1] , , , Stochastic Stratonovich calculus for fractional Brownian motion with Hurst parameter less than , Taiwanese J. Math. 5 (3) (2001) 609-632. | Zbl | MR
[2] , , , Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than , Stochastic Process Appl. 86 (1) (2000) 121-139. | Zbl | MR
[3] , , , Stochastic calculus with respect to Gaussian processes, Ann. Probab. 29 (2) (2001) 766-801. | Zbl | MR
[4] , An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter, Stochastic Process Appl. 104 (1) (2003) 81-106. | Zbl | MR
[5] , Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J. 23 (1973) 69-94. | Zbl | MR
[6] , , , Stochastic integration with respect to fractional Brownian motion, Ann. Inst. H. Poincaré Probab. Statist. 39 (1) (2003) 27-68. | Zbl | MR | Numdam
[7] , , , Tanaka formula for the fractional Brownian motion, Stochastic Process Appl. 94 (2) (2001) 301-315. | Zbl | MR
[8] , , Stochastic analysis, rough path analysis and fractional Brownian motions, Probab. Theory Related Fields 122 (1) (2002) 108-140. | Zbl | MR
[9] , , Stochastic analysis of the fractional Brownian motion, Potential Anal. 10 (2) (1999) 177-214. | Zbl | MR
[10] , , , Stochastic calculus for fractional Brownian motion I. Theory, SIAM J. Control Optim. 38 (2) (2000) 582-612. | Zbl | MR
[11] , , L'integrale stochastique comme opérateur de divergence dans l'espace fonctionnel, J. Funct. Anal. 46 (2) (1982) 230-238. | Zbl | MR
[12] , , , Generalized covariations, local time and Stratonovich Itô’s formula for fractional Brownian motion with Hurst index , Ann. Probab. 31 (4) (2003) 1772-1820. | Zbl
[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] , Probability structure preserving and absolute continuity, Ann. Inst. H. Poincaré 38 (4) (2002) 557-580. | Zbl | MR | Numdam
[15] , , Fractional white noise calculus and applications to finance, Inf. Dim. Anal. Quant. Probab. Rel. Top. 6 (1) (2003) 1-32. | Zbl | MR
[16] , Stochastic integral, Proc. Imperial Acad. Tokyo 20 (1944) 519-524. | Zbl | MR
[17] , Stochastic analysis of fractional Brownian motions, Stochastics Stochastics Rep. 55 (1995) 121-140. | Zbl | MR
[18] , , Theory of Martingales, Kluwer Academic, Dordrecht, 1989. | Zbl | MR
[19] , , Empirical implications of arbitrage-free asset markets, in: (Ed.), Models, Methods and Applications of Econometrics, Blackwell, 1993.
[20] , Stochastic Analysis, Springer, 1997. | Zbl | MR
[21] , , Stochastic integral equations without probability, Bernoulli 6 (3) (2000) 401-434. | Zbl | MR
[22] , The Malliavin Calculus and Related Topics, Springer, 1995. | Zbl | MR
[23] , , Stochastic calculus with anticipating integrands, Probab. Theory Related Fields 78 (4) (1988) 535-581. | Zbl | MR
[24] , , Integration questions related to fractional Brownian motion, Probab. Theory Related Fields 118 (2) (2000) 251-291. | Zbl | MR
[25] , , Are classes of deterministic integrands for fractional Brownian motion on an interval complete?, Bernoulli 7 (6) (2001) 873-897. | Zbl | MR
[26] , Skorohod stochastic integration with respect to non-adapted processes on Wiener space, Stochastics Stochastics Rep. 65 (1998) 13-39. | Zbl | MR
[27] , , Continuous Martingales and Brownian Motion, Springer, 1999. | Zbl | MR
[28] , , Forward, backward and symmetric stochastic integration, Probab. Theory Related Fields 97 (3) (1993) 403-421. | Zbl | MR
[29] , , The generalized covariation process and Itô formula, Stochastic Process Appl. 59 (1) (1995) 81-104. | Zbl | MR
[30] , , Itô formula for -functions of semimartingales, Probab. Theory Related Fields 104 (1) (1996) 27-41. | Zbl | MR
[31] , Arbitrage with fractional Brownian motion, Math. Finance 7 (1) (1997) 95-105. | Zbl | MR
[32] , , , Fractional Integrals and Derivatives, Gordon and Breach, 1993. | Zbl | MR
[33] , An inequality of the Hölder type, connected with Stieltjes integration, Acta Math. (Sweden) 67 (1936) 251-282. | Zbl | MR
[34] , Integration with respect to fractal functions and stochasic calculus. I, Probab. Theory Related Fields 111 (3) (1998) 333-374. | Zbl | MR
Cité par Sources :






