-
Article
Stationary Reversible Processes of a Moving Average and Autorepression with Residuals as a Moving Average
In this paper, we show how to select an adequate model of a stationary reversible moving-average process of finite order, given the appropriate number of sample correlations. We find the admissibility conditio...
-
Article
Classical Kapitsa’s problem of stability of an inverted pendulum and some generalizations
The classical Kapitsa’s problem of stability of an inverted pendulum subjected to vertical vibration of the support and some generalizations are investigated. The asymptotic method of two-scale expansions allo...
-
Article
Linear Kalman–Bucy Filter with Vector Autoregressive Signal and Noise
We consider the linear Kalman–Bucy filter problem for a system in which a signal and a noise are independent vector stationary autoregressive processes with orders higher than 1. Recurrent equations for the fi...
-
Article
Linear Generalized Kalman–Bucy Filters
The linear generalized Kalman–Bucy filter problem has been studied in this work. A sum of a useful signal and a noise is an observed process. A signal and a noise are independent stationary auto-regressive pro...
-
Article
Attraction Basins in the Generalized Kapitsa Problem
The stability of the vertical position of an inverted pendulum under the action of support vibration and the attraction basin of this position are considered. In addition to the classical Kapitsa problem for t...
-
Article
Monte Carlo Method for Solving ODE Systems
The Monte Carlo method is applied to solve Cauchy problems for a system of linear and nonlinear ordinary differential equations. The Monte Carlo method is relevant for the solution of large systems of equation...
-
Article
Linear Kalman–Bucy Filter with Autoregressive Signal and Noise
In the Kalman—Bucy filter problem, the observed process consists of the sum of a signal and a noise. The filtration begins at the same moment as the observation process and it is necessary to estimate the sign...
-
Article
Workspaces of the Stewart platform in the 6D space of generalized coordinates
The kinematics and dynamics of the classical Stewart platform is studied. The platform is a rigid body supported by six rods of variable length. Well-known differential equations describing the motion of the p...
-
Article
The Monte-Carlo algorithm for the solving of systems of linear algebraic equations by the Seidel method
The iteration algorithm is used to solve systems of linear algebraic equations by the Monte-Carlo method. Each next iteration is simulated as a random vector such that its expectation coincides with the Seidel...
-
Article
Vibrations of a floating beam on marine waves
Small vertical vibrations of a horizontal floating towed beam on marine waves are considered. The beam bending stiffness, attached mass of water, and water resistance forces are taken into account. The theory ...
-
Article
Ruin probabilities for an insurance company based on some stochastic risk models
The paper is concerned with a stochastic risk model with independent random claims and premiums. Recurrence formulas for the ruin probabilities of an insurance company at times of claim payments are obtained. ...
-
Article
The impact of the shape of the spectral density of random wave disturbance on the vibrations of a fixed sea-based offshore platform
It was generally assumed earlier in the study of the impact of random wave disturbance on fixed sea-based offshore platforms (FSOP) that the spectral density of wind-driven gravitational waves has the shape de...
-
Article
On solving systems of linear algebraic equations by Gibbs’s method
The paper presents an algorithm of approximate solution of a system of linear algebraic equations by the Monte Carlo method superimposed with ideas of simulating Gibbs and Metropolis fields. A solution in the ...
-
Article
On criteria of estimation of the errors of cubature formulas
The paper considers cubature formulas for calculating integrals of functions f(X), X = (x 1, …, x n ) which are defined on the n-...
-
Article
Calculation of the discrepancy of a finite set of points in the unit n-cube
An algorithm for calculating the discrepancy of finitely many points in the unit n-cube [0, 1]n is suggested. This algorithm is easy to program. For 2 ≤ n ≤ 4, the suggested algorithm is significantly faster than...
-
Article
Estimation of the parameters of the correlation function of a stationary random process
