arXiv subjects
Publications and source records attributed to Elena V. Karachanskaya.
This paper is complete proof of one method for obtaining the generalized Ito-Wentzell formula, its basic idea was announced earlier in a pre-print (arXiv:1309.3038v1). This proof sets the approach which uses the Ito formula and the stochastic approximation theory.
This article studies the dynamics of a finite chain with infinite components. The equation which permits us to find the probability distribution of the chain length is constructed and analysed. This research is a continuation of paper \cite{1}.
Generalization of the Itô-Wentzell formula for the generalized Itô's SDE (Itô's GSDE) system with a non-centered measure is constructed on the basis of the stochastic kernel of integral transformation. The Itô's GSDE system for the kernel the solution of which is the kernel of the integral invariant, is formed. This invariant is connected with the solution of the Itô's GSDE system non-centered measure. The concept of a stochastic first integral of the Itô's GSDE system with non-centered measure is introduced and conditions that when being performed the random function is the first integral of the set Itô's GSDE system are defined.
In article we construct the program control with probability one for a dynamical system with Poisson perturbations.
Generalization of the Itô-Wentzel formula for the generalized Itô's SDEs (Itô's GSDEs) system with not centered measure is constructed. This construction is based on the basis of the stochastic kernel of integral transformation. The Itô's GSDEs system for the kernel of the integral invariant is constructed. The concept of a stochastic first integral of the Itô's GSDEs system with not centered measure is introduced. The conditions for the random function, that it's the first integral of the set Itô's GSDEs system, are defined.