Mishura, Yulia S.; Shevchenko, Georgiy M. Existence and uniqueness of the solution of stochastic differential equation involving Wiener process and fractional Brownian motion with Hurst index \(H > 1/2\). (English) Zbl 1315.60071 Commun. Stat., Theory Methods 40, No. 19-20, 3492-3508 (2011). Summary: We consider a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficients, it is proved that the equation has a unique solution. Cited in 1 ReviewCited in 29 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60G15 Gaussian processes 60G22 Fractional processes, including fractional Brownian motion 60J65 Brownian motion Keywords:Euler approximation; fractional Brownian motion; mixed stochastic differential equation; pathwise integral PDFBibTeX XMLCite \textit{Y. S. Mishura} and \textit{G. M. Shevchenko}, Commun. Stat., Theory Methods 40, No. 19--20, 3492--3508 (2011; Zbl 1315.60071) Full Text: DOI arXiv References: [1] Garsia A. M., Ann. Inst. Fourier 24 pp 67– (1974) · Zbl 0274.26006 · doi:10.5802/aif.507 [2] DOI: 10.1080/07362990802286483 · Zbl 1151.60028 · doi:10.1080/07362990802286483 [3] Kleptsyna M., Probl. Infer. Transm. 34 pp 332– (1998) [4] Kubilius K., Liet. Mat. Rink. 40 pp 104– (2000) [5] DOI: 10.1016/S0304-4149(01)00145-4 · Zbl 1059.60068 · doi:10.1016/S0304-4149(01)00145-4 [6] DOI: 10.1007/978-3-540-75873-0 · Zbl 1138.60006 · doi:10.1007/978-3-540-75873-0 [7] Nualart D., Collect. Math. 53 pp 55– (2002) [8] DOI: 10.1023/A:1018754806993 · Zbl 0970.60045 · doi:10.1023/A:1018754806993 [9] Samko S., Fractional Integrals and Derivatives. Theory and Applications (1993) [10] 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.