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.

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