Stochastic integration with respect to Volterra processes
Annales de l'I.H.P. Probabilités et statistiques (2005)
- Volume: 41, Issue: 2, page 123-149
- ISSN: 0246-0203
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topDecreusefond, L.. "Stochastic integration with respect to Volterra processes." Annales de l'I.H.P. Probabilités et statistiques 41.2 (2005): 123-149. <http://eudml.org/doc/77839>.
@article{Decreusefond2005,
author = {Decreusefond, L.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {fractional calculus; stochastic calculus; fractional Brownian motion},
language = {eng},
number = {2},
pages = {123-149},
publisher = {Elsevier},
title = {Stochastic integration with respect to Volterra processes},
url = {http://eudml.org/doc/77839},
volume = {41},
year = {2005},
}
TY - JOUR
AU - Decreusefond, L.
TI - Stochastic integration with respect to Volterra processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
PB - Elsevier
VL - 41
IS - 2
SP - 123
EP - 149
LA - eng
KW - fractional calculus; stochastic calculus; fractional Brownian motion
UR - http://eudml.org/doc/77839
ER -
References
top- [1] R. Adams, Sobolev Spaces, Academic Press, 1975. Zbl0314.46030MR450957
- [2] E. Alòs, J.O. León, D. Nualart, Stochastic Stratonovitch calculus for fractional Brownian motion with Hurst parameter less than , Taiwanese J. Math.5 (3) (2001) 609-632. Zbl0989.60054MR1849782
- [3] E. Alòs, O. Mazet, D. Nualart, Stochastic calculus with respect to Gaussian processes, Ann. Probab.29 (2) (2001) 766-801. Zbl1015.60047MR1849177
- [4] A. Benassi, P. Bertrand, S. Cohen, J. Istas, Identification d'un processus gaussien multifractionnaire avec des ruptures sur la fonction d'échelle, C. R. Acad. Sci. Paris Sér. I Math.329 (5) (1999) 435-440. Zbl0947.62054MR1710087
- [5] 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
- [6] L. Coutin, Z. Qian, Stochastic differential equations for fractional Brownian motions, C. R. Acad. Sci. Paris Sér. I Math.331 (1) (2000) 75-80. Zbl0981.60040MR1780221
- [7] W. Dai, C.C. Heyde, Itô's formula with respect to fractional Brownian motion and its application, J. Appl. Math. Stochastic Anal.9 (4) (1996) 439-448. Zbl0867.60029MR1429266
- [8] L. Decreusefond, Stochastic calculus for Volterra processes, C. R. Acad. Sci. Paris Sér. I Math.334 (10) (2002) 903-908. Zbl1074.60066
- [9] L. Decreusefond, A. Üstünel, Application du calcul des variations stochastiques au mouvement brownien fractionnaire, C. R. Acad. Sci. Paris Sér. I Math.321 (12) (1995) 1605-1608. Zbl0846.60057MR1367815
- [10] L. Decreusefond, A. Üstünel, Stochastic analysis of the fractional Brownian motion, Potential Anal.10 (2) (1999) 177-214. Zbl0924.60034MR1677455
- [11] Doukhan P., Oppenheim G., Taqqu M. (Eds.), Long Range Dependence: Theory and Applications, Birkhäuser, 2002, pp. 203-226, Chapter 10.
- [12] M. Errami, F. Russo, Covariation de convolution de martingales, C. R. Acad. Sci. Paris Sér. I Math.326 (5) (1998) 601-606. Zbl0917.60054MR1649341
- [13] M. Errami, F. Russo, n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes, Stochastic Process. Appl.104 (2) (2003) 259-299. Zbl1075.60531MR1961622
- [14] D. Feyel, A. de La Pradelle, Capacités gaussiennes, Ann. Inst. Fourier41 (1) (1991) 49-76. Zbl0735.46018MR1112191
- [15] D. Feyel, A. de La Pradelle, On fractional Brownian processes, Potential Anal.10 (3) (1999) 273-288. Zbl0944.60045MR1696137
- [16] D. Feyel, A. de la Pradelle, The FBM Ito's formula through analytic continuation, Electron. J. Probab.6 (26) (2001) 22, (electronic). Zbl1008.60074MR1873303
- [17] M. Gradinaru, F. Russo, P. Vallois, Generalized covariations, local time and Stratonovich Itô’s formula for fractional Brownian motion with Hurst index , Ann. Probab.31 (4) (2003) 1772-1820. Zbl1059.60067
- [18] T.J. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana14 (2) (1998) 215-310. Zbl0923.34056MR1654527
- [19] A. Nikiforov, V. Uvarov, Special Functions of Mathematical Physics, Birkhäuser, 1988. Zbl0624.33001MR922041
- [20] D. Nualart, The Malliavin Calculus and Related Topics, Springer-Verlag, 1995. Zbl0837.60050MR1344217
- [21] S. Samko, A. Kilbas, O. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, 1993. Zbl0818.26003MR1347689
- [22] J. Tambaca, Estimates of the Sobolev norm of a product of two functions, J. Math. Anal. Appl.255 (1) (2001) 137-146. Zbl0979.46020MR1813814
- [23] A.S. Üstünel, The Itô formula for anticipative processes with nonmonotonous time scale via the Malliavin calculus, Probab. Theory Related Fields79 (1988) 249-269. Zbl0635.60059MR958290
- [24] A.S. Üstünel, An Introduction to Analysis on Wiener Space, Lectures Notes in Mathematics, vol. 1610, Springer-Verlag, 1995. Zbl0837.60051MR1439752
- [25] A.S. Üstünel, M. Zakai, Transformations of Measure on Wiener Spaces, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2000. Zbl0974.46044MR1736980
- [26] M. Zähle, Integration with respect to fractal functions and stochastic calculus, I, Probab. Theory Related Fields111 (3) (1998) 333-374. Zbl0918.60037MR1640795
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