Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
40
7
2008
Absolute Stability in Mean-Square of the Lourie−Ito−Skorokhod Stochastic Differential Equation
1-8
Lyubov I.
Yasinskaya
Chernovtsy National Yu. Fedkovich University, Chernovtsy, Ukraine
Andrey Ya.
Dovgun
Bukovinskaya State Financial Academy, Chernovtsy, Ukraine
We obtained sufficient conditions of absolute stability in mean-square of the zero solution of the Lourie−Ito−Skorokhod stochastic differential equation, which are under diffusion and Poisson perturbations. We generalized the result of D.G. Korenevskiy in the case of more general stochastic differential equations, which strong solutions belong to the Skorokhod space of right continuous functions, which have left-hand limits.
Stochastic Dynamics of Oscillator Drift in Media with Spatially Nonhomogeneous Friction
9-25
Mikhail A.
Ivanov
G.V. Kurdyumov Institute of Metallophysics of National Academy of Sciences of Ukraine, Kiev, Ukraine
Vladimir A.
Dobrynskiy
G.V. Kurdyumov Institute of Metallophysics of National Academy of Sciences of Ukraine, Kiev, Ukraine
A mathematical model of forced oscillation dynamics of a stochastic oscillator on a plane with a nonlinear nonhomogeneous friction has been created. The dynamics of the oscillator Brownian walk which appears under a noise action in the direction orthogonal to direction of external driving force has been studied. A dependence of energy dissipation by the given oscillator on its Brownian walk dynamics has been determined.
Problems of Interpretation and Experimental Data Assimilation
26-36
Vyacheslav F.
Gubarev
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev, Ukraine
Most of inverse problems dealing with interpretation of data obtained in experiment are known as ill-posed ones. Using regularization approach consideration was given to the statements of these problems based on the variational principle. This allows one to obtain approximate solutions which are consistent with errors in initial data and moreover, to perform measurement data assimilation into a mathematical model of the object under investigation.
On Identification of Linear Stationary Systems
37-47
Alexander S.
Apostolyuk
National Technical University of Ukraine "Kiev Polytechnical Institute", Kiev, Ukraine
Vladimir B.
Larin
S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
We consider the algorithm for identification of linear stationary systems by results of measurement of transient process. This algorithm can be treated as nonlinear analog of the Prony method. Similar to the Prony method the suggested algorithm makes it possible to realize decomposition of the initial problem of identification, however, it eliminates from consideration the intermediate linear model with discrete time, which is used in the Prony method. Generalization of the algorithm is adduced in the case when some roots of the characteristic polynomial of the identified system are known. By the before published examples we conduct comparison of accuracy of estimates obtained by the suggested method and other known methods for solving this problem.
Sweep Algorithm for Solving Discrete Optimal Control Problems with Three-point Boundary Conditions
48-58
Fikret Akhmed Ali Ogly
Aliev
Scientific Research Institute of Applied Mathematics of Baku State University, Azerbaijan
Rena Takhir kyzy
Zulfugarova
Research Institute of Applied Mathematics of Baku State University (Azerbaijan)
Mutallim Mirzaakhmed ogly
Mutallimov
Scientific Research Institute of Applied Mathematics of Baku State University, Azerbaijan
The sweep algorithm for solving optimal control problem with three-point boundary conditions is offered. According to this algorithm the search for initial conditions is reduced to solution of the corresponding system of linear algebraic equations. Analogous algorithm is proposed for a discrete case.
The Cournot−Nash Equilibrium under Mutual Uncertainty
59-72
Vasiliy M.
Gorbachuk
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
The role of planning and forecasting by the example of companies behaviour under asymmetric uncertainty is shown. The company with a more narrow range of uniform distribution for outputs becomes leader, and a company with a broader range of outputs becomes a follower while generalized Cournot−Stackelberg−Nash equilibrium. The equilibrium profit of a leader is greater than the equilibrium profit of a follower.
On Approximation of Smooth Functions by L-Splines at a Point
73-80
Zhanna V.
Khudaya
Dneprodzerzhinsk State Technical University, Dneprodzerzhinsk, Ukraine
We constructed "almost interpolation" generalized L-splines based on the basis functions, composed of parts of solutions of the differential equation, which coefficients change from segment to segment. Estimate of error for approximation by these splines of smooth functions at arbitrary point were obtained and we proved superconvergence in nodes of spline, which approximates functions holding the same differential equation as the built splines.