×

zbMATH — the first resource for mathematics

The rate of convergence for Euler approximations of solutions of stochastic differential equations driven by fractional Brownian motion. (English) Zbl 1154.60046
Authors’ abstract: The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of solutions of pathwise SDEs driven by fBm with Hurst index \(H>1/2\) can be estimated by \(O(\delta ^{2H-1})\) , where \(\delta \) is the diameter of partition used for discretization. For discrete-time approximations of Skorohod-type quasilinear equation driven by fBm we prove that the rate of convergence is \(O(\delta^H)\) .

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G18 Self-similar stochastic processes
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] DOI: 10.1111/1467-9965.00018 · Zbl 1069.91047 · doi:10.1111/1467-9965.00018
[2] Grecksch W., Z. Anal. Anwendungen 17 pp 715– (1998)
[3] Holden H., Stochastic Partial Differential Equations. A Modeling, White Noise Functional Approach (1996)
[4] DOI: 10.1142/S0219025703001110 · Zbl 1045.60072 · doi:10.1142/S0219025703001110
[5] Kloeden P.E., Numerical Solution of Stochastic Differential Equations (1992) · Zbl 0752.60043 · doi:10.1007/978-3-662-12616-5
[6] Kohatsu-Higa A., Stochastic Analysis on Infinite-Dimensional Spaces 310 pp 141– (1994)
[7] Mishura Y.S., Teor. Imovirn. Mat. Stat. pp 95– (2003)
[8] Nourdin I., C. R., Math. Acad. Sci. Paris 340 pp 611– (2005)
[9] DOI: 10.1007/s10959-007-0083-0 · Zbl 1141.60043 · doi:10.1007/s10959-007-0083-0
[10] Nualart D., Collect. Math. 53 pp 55– (2000)
[11] DOI: 10.1007/s004400050171 · Zbl 0918.60037 · doi:10.1007/s004400050171
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.