An application of the nonselfadjoint operators theory in the study of stochastic processes
In the present paper, a stochastic process is considered as a solution of an operatorial system. Using the triangular model, the correlation function of a nonstationary linearly representable stochastic process for which the corresponding operator has some specific properties is obtained. The study is made in the case when the corresponding spectrum is purely real nonconcentrated at zero. First, the case when the spectrum is concentrated at a unique point different from zero is presented. The correlation function when the spectrum is finite is obtained. In the general case, the correlation function and the infinitesimal correlated function are given as limits of sequences of correlated functions and, respectively, infinitesimal correlated functions, corresponding to a sequence of complex Gaussian stochastic processes. The result obtained here is valid for stochastic fields as well as for curves or surfaces in arbitrary Hilbert spaces.
scientific article; zbMATH DE number 2166661