Tleubergenov M. I.
Ukr. Mat. Zh. - 2019. - 71, № 1. - pp. 139-145
Using the quasi-inversion method we obtain necessary and sufficient conditions for the solvability of the main (according to Galiullin’s classification) inverse problem in the class of first-order Itˆo stochastic differential systems with random perturbations from the class of processes with independent increments, with diffusion degenerate in a part of variables and with given properties, depending on a part of variables.
On the solution of the problem of stochastic stability of the integral manifold by the Lyapunov’s second method
Ukr. Mat. Zh. - 2016. - 68, № 1. - pp. 14-27
By using the method of Lyapunov functions, we establish sufficient conditions of stability and asymptotic stability in probability for the integral manifold of the Itˆo differential equations in the presence of random perturbations from the class of processes with independent increments. Theorems on the stochastic stability of the analytically given integral manifold of differential equations are proved in the first approximation and under the permanent action of small (in the mean) random perturbations.
Ukr. Mat. Zh. - 2013. - 65, № 5. - pp. 712–716
The separation method is used obtain sufficient conditions for the solvability of the main (according to Galiullin’s classification) inverse problem in the class of first-order Itô stochastic differential systems with random perturbations from the class of Wiener processes and diffusion degenerate with respect to a part of variables.
On the construction of a set of stochastic differential equations on the basis of a given integral manifold independent of velocities
Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 1002–1008
We construct the Lagrange equation, Hamilton equation, and Birkhoff equation on the basis of given properties of motion under random perturbations. It is assumed that random perturbation forces belong to the class of Wiener processes and that given properties of motion are independent of velocities. The obtained results are illustrated by an example of motion of an Earth satellite under the action of gravitational and aerodynamic forces.
Ukr. Mat. Zh. - 1995. - 47, № 3. - pp. 307–314
Rank conditions for control of linear pulse systems are established. The Pontryagin maximum principle is obtained in sufficient form. An example of control synthesis in a problem for linear pulse systems is given.