PARAMETRIC MODELS OF NONSTATIONARY GAUSSIAN-PROCESSES

Three parametric representations are developed for approximating a gen eral nonstationary Gaussian process X(t). The representations: (1) are based on the Bernstein and other interpolation polynomials, spline fu nctions, and an extension of a sampling theorem for stationary process es; (2) consist of finite sums of specified deterministic functions wi th random amplitudes depending on X(t); and (3) converge to X(t) as th e number of these functions increases However, their convergence rates differ. Numerical results for a nonstationary Ornstein-Uhlenbeck proc ess show that the interpolation polynomials have the slowest rate of c onvergence. The parametric representations based on spline functions a nd the extended sampling theorem have similar convergence rates The pa per also presents methods for generating realizations of X(t) based on the three parametric models of this process.