Evaluation of expectation of a functionals depending on the solution of linear stochastic equations

The method for evaluation of expectation of a functionals depending on the solution of linear stochastic differential equations is proposed. This method is based on evaluation of the eigenvalues of a three-diagonal matrix using the Sturm sequences. It is considered the application of this method to evaluation of characteristics of Ising systems with random effect in the form of a random white noise process.