Reconstruction of random-disturbance amplitude in linear stochastic equations from measurements of some of the coordinates

The problem of reconstructing the unknown amplitude of a random disturbance in a linear stochastic differential equation is studied in a fairly general formulation by applying dynamic inversion theory. The amplitude is reconstructed using discrete information on several realizations of some of the coordinates of the stochastic process. The problem is reduced to an inverse one for a system of ordinary differential equations satisfied by the elements of the covariance matrix of the original process. Constructive solvability conditions in the form of relations on the parameters of the system are discussed. A finite-step software implementable solving algorithm based on the method of auxiliary controlled models is tested using a numerical example. The accuracy of the algorithm is estimated with respect to the number of measured realizations.