Tetiana Ianevych

National Taras Shevchenko University of Kyiv | Київський національний університет імені Тараса Шевченка · Department of Probability Theory, Statistics and Actuarial Mathematics

The paper is devoted to one possible way of the model construction for the stationary Gaussian process with given accuracy and reliability in functional space C ⁢ ( [ 0 , T ] ) .

In the paper, we consider the problem of simulation of a strictly φ-sub-Gaussian generalized fracti-onal Brownian motion. Simulation of random processes and fields is used in many areas of natural and social sciences. A special place is occupied by methods of simulation of the Wiener process and fractional Brownian motion, as these processes are wi...

In this paper, we had constructed the goodness-of-fit tests incorporating several components, like expectation and covariance function, for identification of a non-centered stationary Gaussian stochastic process. For the construction of the corresponding estimators and investigation of their properties we had utilized the theory of Square Gaussian...

In this paper, we continue to study the properties of a separable strictly φ-sub-Gaussian quasi shot noise process $X(t) = \int_{-\infty}^{+\infty} g(t,u) d\xi(u), t\in\R$, generated by the response function g and the strictly φ-sub-Gaussian process ξ = (ξ(t), t ∈ R) with uncorrelated increments, such that E(ξ(t)−ξ(s))^2 = t−s, t>s ∈ R. We consider...

Two methods of modeling for the Ornstein-Uhlenbeck process are studied in the work. This process has many applications in physics, financial mathematics, biology. Therefore, it is extremely important to have instruments for modeling this process to solve various theoretical and practical tasks. The peculiarity of this process is that it has many in...

In this paper we have constructed the goodness-of-fit tests incorporating several components, like expectation and covariance function for identification of a non-centered univariate random sequence or auto-covariances and cross-covariances for identification of a centered multivariate random sequence. For the construction of the corresponding esti...

In this paper we had made an attempt to incorporate the results from the theory of square Gaussian random variables in order to construct the goodness of fits test for random sequences (time series). We considered two versions of such tests. The first one was designed for testing the adequacy of the hypotheses on expectation and covariance function...