Fractional Brownian motion Malliavin calculus Almost sure exponential stability Anticipating initial condition Averaging principle Backward stochastic differential equations Burgers-KPZ type nonlinear equations in infinite dimensions Characterization theorem Convergence rate Density estimate Distribution dependent stochastic differential equations Fast–slow forward–backward stochastic differential equations Fourier–Besov spaces Fractional derivative of Riemann-Liouville type Fréchet differentiation Galerkin approximation Gaussian processes Girsanov transformation Lévy generators Lévy noise Moment exponential stability No free lunch with vanishing risk condition Stability Stochastic averaging principle Stochastic fractional Navier–Stokes equation Stochastic fractional differential equations with non-Lipschitz coefficients Stochastic nematic liquid crystals flows Stochastic stability Strong solutions Time-changed Brownian motions