Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter $H\in (0,\frac{1}{2})$

 Access to full text

 Full (PDF)

1. [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. Zbl0989.60054MR1849782
2. [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. Zbl1028.60047MR1741199
3. [3] E. Alòs, O. Mazet, D. Nualart, Stochastic calculus with respect to Gaussian processes, Ann. Probab.29 (2) (2001) 766-801. Zbl1015.60047MR1849177
4. [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. Zbl1075.60530MR1956473
5. [5] S. Berman, Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J.23 (1973) 69-94. Zbl0264.60024MR317397
6. [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. Zbl1016.60043MR1959841
7. [7] L. Coutin, D. Nualart, C.A. Tudor, Tanaka formula for the fractional Brownian motion, Stochastic Process Appl.94 (2) (2001) 301-315. Zbl1053.60055MR1840834
8. [8] L. Coutin, Z. Qian, Stochastic analysis, rough path analysis and fractional Brownian motions, Probab. Theory Related Fields122 (1) (2002) 108-140. Zbl1047.60029MR1883719
9. [9] L. Decreusefond, A.S. Üstünel, Stochastic analysis of the fractional Brownian motion, Potential Anal.10 (2) (1999) 177-214. Zbl0924.60034MR1677455
10. [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. Zbl0947.60061MR1741154
11. [11] B. Gaveau, P. Trauber, L'integrale stochastique comme opérateur de divergence dans l'espace fonctionnel, J. Funct. Anal.46 (2) (1982) 230-238. Zbl0488.60068MR660187
12. [12] M. Gradinaru, F. Russo, P. Vallois, Generalized covariations, local time and Stratonovich Itô’s formula for fractional Brownian motion with Hurst index $H\ge 1/4$, Ann. Probab.31 (4) (2003) 1772-1820. Zbl1059.60067
13. [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. Zbl1083.60045
14. [14] Y. Hu, Probability structure preserving and absolute continuity, Ann. Inst. H. Poincaré38 (4) (2002) 557-580. Zbl1002.60046MR1914939
15. [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. Zbl1045.60072MR1976868
16. [16] K. Itô, Stochastic integral, Proc. Imperial Acad. Tokyo20 (1944) 519-524. Zbl0060.29105MR14633
17. [17] S.J. Lin, Stochastic analysis of fractional Brownian motions, Stochastics Stochastics Rep.55 (1995) 121-140. Zbl0886.60076MR1382288
18. [18] Sh.R. Liptser, A.N. Shiryaev, Theory of Martingales, Kluwer Academic, Dordrecht, 1989. Zbl0728.60048MR1022664
19. [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. [20] P. Malliavin, Stochastic Analysis, Springer, 1997. Zbl0878.60001MR1450093
21. [21] T. Mikosch, R. Norvaiša, Stochastic integral equations without probability, Bernoulli6 (3) (2000) 401-434. Zbl0963.60060MR1762553
22. [22] D. Nualart, The Malliavin Calculus and Related Topics, Springer, 1995. Zbl0837.60050MR1344217
23. [23] D. Nualart, E. Pardoux, Stochastic calculus with anticipating integrands, Probab. Theory Related Fields78 (4) (1988) 535-581. Zbl0629.60061MR950346
24. [24] V. Pipiras, M.S. Taqqu, Integration questions related to fractional Brownian motion, Probab. Theory Related Fields118 (2) (2000) 251-291. Zbl0970.60058MR1790083
25. [25] V. Pipiras, M.S. Taqqu, Are classes of deterministic integrands for fractional Brownian motion on an interval complete?, Bernoulli7 (6) (2001) 873-897. Zbl1003.60055MR1873833
26. [26] N. Privault, Skorohod stochastic integration with respect to non-adapted processes on Wiener space, Stochastics Stochastics Rep.65 (1998) 13-39. Zbl0918.60038MR1708428
27. [27] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, 1999. Zbl0917.60006MR1725357
28. [28] F. Russo, P. Vallois, Forward, backward and symmetric stochastic integration, Probab. Theory Related Fields97 (3) (1993) 403-421. Zbl0792.60046MR1245252
29. [29] F. Russo, P. Vallois, The generalized covariation process and Itô formula, Stochastic Process Appl.59 (1) (1995) 81-104. Zbl0840.60052MR1350257
30. [30] F. Russo, P. Vallois, Itô formula for $C^1$-functions of semimartingales, Probab. Theory Related Fields104 (1) (1996) 27-41. Zbl0838.60045MR1367665
31. [31] L.C.G. Rogers, Arbitrage with fractional Brownian motion, Math. Finance7 (1) (1997) 95-105. Zbl0884.90045MR1434408
32. [32] F.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach, 1993. Zbl0818.26003MR1347689
33. [33] L.C. Young, An inequality of the Hölder type, connected with Stieltjes integration, Acta Math. (Sweden)67 (1936) 251-282. Zbl0016.10404MR1555421
34. [34] M. Zähle, Integration with respect to fractal functions and stochasic calculus. I, Probab. Theory Related Fields111 (3) (1998) 333-374. Zbl0918.60037MR1640795

1. Ivan Nourdin, David Nualart, Ciprian A. Tudor, Central and non-central limit theorems for weighted power variations of fractional brownian motion
2. David Nualart, Stochastic calculus with respect to fractional Brownian motion
3. Laure Coutin, Nicolas Victoir, Enhanced Gaussian processes and applications
4. J. Šnupárková, Weak solutions to stochastic differential equations driven by fractional Brownian motion