Before revision:  We apply our results to specific examples of such models -- multiplicative, Heston , and combined multiplicative-Heston -- and use historic stock market data to obtain parameters of their steady-state distributions and cross-correlations between Weiner processes in the models for stock returns and stochastic variance .
After revision:  We apply our results to specific examples of such models -- multiplicative, Heston , and combined multiplicative-Heston -- and use historic stock market data to obtain parameters of their steady-state probability density functions are Gamma, Inverse Gamma and Beta Prime respectively, the latter two exhibiting "fat" tails. For the Heston model, we apply the eigenvalue analysis of the Fokker-Planck equation to derive the correlation function -- in agreement with the general analysis -- and to identify a series of time scales, which are observable in relaxation of cumulants on approach to the steady state. We test our findings on a very large set of historic financial markets data .