On some fractional stochastic delay differential equations

We consider the Cauchy problem for an abstract stochastic delay differential equation driven by fractional Brownian motion with the Hurst parameter H>12. We prove the existence and uniqueness for this problem, when the coefficients have enough regularity, the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of any order. We prove the theorem by using the convergence of the Picard–Lindelö f iterations in L2(Ω)L2(Ω) to a solution of this problem which admits a smooth density with respect to Lebesgue’s measure on RR.