I was recently reading Numerical Solution of Stochastic Differential Equations by Kloeden and Platen and trying the understand the linearisation of an SDE to determine its Lyapunov exponents.
However, the text recommends linearising around a "stochastically stationary solution" of the SDE. What does this mean? I understand that the corresponding Fokker-Planck equation may posses a stationary solution, as a distribution. But since a solution of the SDE is just a trajectory, what does the stochastically stationary solution mean?
Is it simply a point at which both the drift and diffusion coefficients are both zero?