Statistical estimation of distributions of random coefficients in the Langevin stochastic differential equation

A method is described for statistical estimation of the distributions of random coefficients of the Langevin stochastic differential equation (SDE) by the technique of moving separation of mixtures. Discrete approximations are proposed for these distributions. For the purpose of study of variability of the distributions of the SDE coefficients in time, an algorithm is proposed for sequential identification (determination of local connectivity) of the components of the resulting mixture distributions. This algorithm is based on combining a greedy algorithm for the determination of the number of components with a lustering method ($k$- or $c$-means). The application of the proposed method is illustrated by particular examples of the analysis of processes of heat transfer between atmosphere and ocean.