×

zbMATH — the first resource for mathematics

Operators associated with a stochastic differential equation driven by fractional Brownian motions. (English) Zbl 1119.60043
Rough paths theory is used in studying operators associated to stochastic differential equations driven by fractional Brownian motion.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Baudoin, F., An introduction to the geometry of stochastic flows, (2004), Imperial College Press · Zbl 1085.60002
[2] Arous, G.B., Flots et séries de Taylor stochastiques, Probab. theory related fields, 81, 29-77, (1989) · Zbl 0639.60062
[3] Borell, C., On polynomial chaos and integrability, Probab. math. statist., 3, 2, 191-203, (1984) · Zbl 0555.60008
[4] Castell, F., Asymptotic expansion of stochastic flows, Probab. theory related fields, 96, 225-239, (1993) · Zbl 0794.60054
[5] P. Cheridito, D. Nualart, Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H in (0, 1/2), preprint · Zbl 1083.60027
[6] L. Coutin, P. Friz, N. Victoir, Good rough path sequences and applications to anticipating and fractional stochastic calculus, 2005, preprint · Zbl 1132.60053
[7] Coutin, L.; Qian, Z., Stochastic rough path analysis and fractional Brownian motion, Probab. theory related fields, 122, 108-140, (2002) · Zbl 1047.60029
[8] Doss, H., Lien entre équations différentielles stochastiques et ordinaires, Ann. inst. H. Poincaré probab. statist., 13, 99-125, (1977) · Zbl 0359.60087
[9] Fernique, X.M., Régularité des trajectoires des fonctions aléatoires gaussiennes, ecole d’été de probabilités de saint-flour, Lecture note in math., 480, 1-96, (1974)
[10] Hairer, M., Ergodicity of stochastic differential equations driven by fractional Brownian motion, Ann. probab., 33, 3, 703-758, (2005) · Zbl 1071.60045
[11] Lyons, T., Differential equations driven by rough signals, Rev. mat. iberioamericana, 14, 2, 215-310, (1998) · Zbl 0923.34056
[12] Lyons, T.; Qian, Z., System control and rough paths, (2002), Oxford Science Publications · Zbl 1029.93001
[13] I. Nourdin, One-dimensional differential equations driven by a fractional Brownian motion with any Hurst index \(H \in(0, 1)\), 2003, preprint
[14] I. Nourdin, A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension one, 2005, preprint · Zbl 1148.60034
[15] Nualart, D.; Răsçanu, A., Differential equations driven by fractional Brownian motion, Collect. math., 53, 1, 55-81, (2002) · Zbl 1018.60057
[16] Rogers, L.C.G.; Williams, D., Diffusions, Markov processes and martingales, vol. 1, (2000), Cambridge University Press
[17] Strichartz, R.S., The campbell – baker – hausdorff – dynkin formula and solutions of differential equations, J. funct. anal., 72, 320-345, (1987) · Zbl 0623.34058
[18] Süssmann, H., On the gap between deterministic and stochastic ordinary differential equations, Ann. probab., 6, 19-41, (1978) · Zbl 0391.60056
[19] Young, L.C., An inequality of the Hölder type connected with Stieltjes integration, Acta math., 67, 251-282, (1936) · Zbl 0016.10404
[20] Zähle, M., Integration with respect to fractal functions and stochastic calculus I, Probab. theory related fields, 111, 333-374, (1998) · Zbl 0918.60037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.