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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

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.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G15 Gaussian processes
60G22 Fractional processes, including fractional Brownian motion
60J65 Brownian motion
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[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
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