Mixed Stochastic Differential Equations With Long-Range Dependence: Existence, Uniqueness And Convergence Of Solutions

For a mixed stochastic differential equation involving standard Brownian motion and an almost surely Hölder continuous process Z with Hölder exponent γ>1/2, we establish a new result on its unique solvability. We also establish an estimate for difference of solutions to such equations with different processes Z and deduce a corresponding limit theorem. As a by-product, we obtain a result on existence of moments of a solution to a mixed equation under an assumption that Z has certain exponential moments.