Characterisation of Exponential Convergence to Nonequilibrium Limits for Stochastic Volterra Equations

X 0 X0, 1.1b to a nontrivial random variable. Here the solution X is an n-dimensional vector-valued function on 0,∞ , A is a real n × n-dimensional matrix, K is a continuous and integrable n × n-dimensional matrix-valued function on 0,∞ , f is a continuous n-dimensional vectorvalued function on 0,∞ , Σ is a continuous n × d-dimensional matrix-valued function on 0,∞ and B t B1 t , B2 t , . . . , Bd t , where each component of the Brownian motion is independent. The initial condition X0 is a deterministic constant vector. The solution of 1.1a 1.1b can be written in terms of the solution of the resolvent equation