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.


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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