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We prove an existence and uniqueness result of mild solution for a system of stochastic semilinear differential equations with fractional Brownian motions and Hurst parameter  H  &lt; 1∕2. Our approach is based on Perov’s fixed point theorem, and we establish the transportation inequalities, with respect to the uniform distance, for the law of the mild solution.

Transportation inequalities for coupled systems of stochastic delay evolution equations with a fractional Brownian motion