Rozora I. Statistical properties of the estimators of im- pulse response functions

The thesis is devoted to the study of stochastic continuous linear time invariant systems driven by impulse response functions. For the investigation of such systems, the theory of Square-Gaussian stochastic processes is used and continued to develop. In the manuscript the estimation of the probability of overrunning by Square-Gaussian process the level specified by continuous function is obtained. The sufficient conditions of the sampling uniform continuity with probability one are received for Square-Gaussian stochastic process. The distribution of modulus of continuity for the Square-Gaussian process is found. The estimates for the distribution of the tails of Square-Gaussian processes in the norm of continuous functions are improved from existing ones. We study casual time invariant system driven by impulse response function with input signals that are real-valued stationary Gaussian centered stochastic processes with known spectral densities. The convergence rates for the estimator of impulse response function in functional spaces are obtained that allow to construct criteria on the shape of the impulse response function. The conditions on uniform sampling continuity with probability one for the estimator of impulse response function are investigated.