Transportation inequalities for distribution-dependent SDEs driven by fractional Brownian motion and standard Brownian motion

This paper studies distribution-dependent stochastic differential equations driven jointly by a standard Brownian motion and a fractional Brownian motion with Hurst parameter H∈(0,1). By using a joint Girsanov transformation for the underlying Brownian noises, we establish quadratic transportation cost inequalities for the law of the solution under both the uniform metric and the L2-metric. The cases H>1/2 and H<1/2 are treated separately according to the different properties of the Volterra kernel.