EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS TO MIXED-TYPE STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY THE FRACTIONAL BROWNIAN MOTIONS WITH HURST INDICES 𝐻 > 1/4

In this paper there is investigated the problem of unique solvability of the Caushy problem for the mixed type stochastic differential equation driven by the standard Brownian motion and fractional Brownian motions with Hurst indices 𝐻 > 1/4. We prove a theorem on the existence and uniqueness of strong solutions to the mentioned mixed type stochastic differential equations.