A note on exponential stability of non-autonomous linear stochastic differential delay equations driven by a fractional Brownian motion with Hurst index >12

We prove a criterion for the almost sure exponential stability of the scalar non-autonomous linear stochastic differential delay equations driven by a fractional Brownian motion with Hurst index >1∕2. To do that, we need a version of existence and uniqueness of the solution for non-autonomous linear system.