Spline stochastic processes

A definition of spline stochastic processes is given in this paper. We show that an interpolation of discrete stationary stochastic processes by splines does not lead to a continous stationary stochastic process. Randomization is neccessary in order to get a stationary stochastic process. Than we discuss properties of these spline stochastic processes. We relate the statistics of the discrete stochastic process to the statistics of the spline stochastic process. Application of spline stochastic processes to problem of simulation and estimation of signal spectra are discussed.