Existence and Uniqueness of Strong Solutionsof Mixed-Type Stochastic Differential Equations Drivenby Fractional Brownian Motions with HurstExponents $$H>1/4$$

We study the unique solvability of the Cauchy problem for a mixed-type stochastic differential equation driven by the standard Brownian motion and fractional Brownian motions with Hurst exponents $$H>1/4$$ . We prove a theorem on the existence and uniqueness of strong solutions of these stochastic differential equations.