Fisher information bounds for McKean-Vlasov SDEs driven by fractional Brownian motion with small noise

In this paper, we consider the following McKean-Vlasov SDE driven by fractional Brownian motion with small noise [Formula: see text] where the initial condition [Formula: see text] is a real number, [Formula: see text] denotes the law of [Formula: see text], [Formula: see text] is a fractional Brownian motion with Hurst index [Formula: see text] and [Formula: see text] is a small parameter. We study the rate of Fisher information convergence in the central limit theorem for the solution of small noise SDE, then we show that the convergence rate [Formula: see text] is of optimal order.