Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Here, the existence and measurability of solutions for stochastic differential equations driven by fractional Brownian noise with Hurst parameter greater than 1 2 is proved. Our method is based on approximating the main equation by delayed equations as in Peano’s method in ODEs. This method makes the proofs easier and needs weaker assumptions for the existence part, compared with the previous works as in [25]. In addition the constructive nature of the proofs helps to develop some numerical methods for solving such SDEs.