Buldygin V.V.

The equivalence and singularity conditions of gaussian-markov distributions

This paper deals with necessary and sufficient conditions for equivalence and singularity of Gaussian- Markov distributions in R ∞ and l 2 -spaces. The obtained results are of a very simple kind. This allows describing the set of admissible shift of Gaussian- Markov distributions in R ∞ and l 2 -spaces. In addition, the corresponding Radon-Nicodym density is determined.

The asymptotic behaviour of the solutions of stochastic differential equations

In this paper, we study the asymptotic behaviour of the solutions of some stochastic differential equations with the coefficients, dependent on time dη(t)=g(η(t))φ(t)dt + σ(η(t))θ(t)dw(t), η(0)≡b. Moreover, we define the conditions on the functions g, φ, σ, θ, under which the asymptotic behaviour of the solution η coincides with the solution μ of the differential equation dμ(t)=g(μ(t))φ(t)dt, μ(0)≡b.

On correlation properties of the cross-correlogram estimators of impulse response functions

Statistical estimators of unit impulse responses of linear systems under perturbations by Gaussian processes which are different from the white noise are considered. Some properties of correlation functions of estimators are studied in the case when the impulse response function is from the space L2(R).

On asymptotic properties of the crosscorrelogram estimators of impulse response functions in linear systems

In this paper, we consider the cross-correlogram estimators of impulse response functions in linear systems. We hypothesize that the system is disturbed by a family of Gaussian processes close to white noise. We study the asymptotic normality of finite-dimensional distributions of estimators and their asymptotic normality in the space of continuous functions given that the impulse response function belongs to L2R

Some asymptotic properties of dispersion matrices of the estimation error for kalman-bjusy filters

This paper deals with asymptotic properties of some Kalman-Bjusy filters. We also consider the conditions of convergence of dispersion matrices sequence of the estimation error and the properties of the limit matrix.