  Thesis is devoted to the application of cumulant analysis in the estimation
of impulse response functions for continuous time-invariant linear systems,
including systems with inner noises. The main assumption of the work is the
second-order integration of the impulse response function. Our study deals with
cumulant analysis of sample cross-correlograms between stationary Gaussian
stochastic processes. An important role was played by integral representations
for the higher-order cumulants of these second-order statistics. Using the
diagram formula, all representations are reduced to the finite sums of
integrals involving cyclic products of kernels. In the work we proved the
convergence to zero of the corresponding integrals. Then, since the Gaussian
distribution is uniquelly determined by its cumulants and also all higher-order
cumulants of the estimators tend to zero, we establish the asymptotic normality
of the integral-type cross-correlogram estimators.
