The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of solutions of pathwise SDEs driven by fBm with Hurst index H>1/2 can be estimated by , where δ is the diameter of partition used for discretization. For discrete-time approximations of Skorohod-type quasilinear equation driven by fBm we prove that the rate of convergence is .

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.

In this paper, we consider a stochastic differential equation driven by a fractional Brownian motion and a Wiener process and having jumps. We prove that this equation has a unique solution and show that all moments of the solution are finite.

We consider a stochastic delay differential equation driven by a Hölder continuous process $Z$ and a Wiener process. Under fairly general assumptions on coefficients of the equation, we prove that it has a unique solution. We also give a sufficient condition for finiteness of moments of the solution and prove that the solution depends on $Z$ continuously.