Abstract
Background. Asymptotic behavior at infinity of non-autonomous stochastic differential equation solutions is studied in the paper. Objective. The aim of the work is to find sufficient conditions for the strong law of large numbers for a random process which is a solution of non-autonomous stochastic differential equation.Methods. Basic results of the theory of stochastic differential equations related to stochastic integrals estimation.Results. Sufficient conditions for almost sure convergence to zero of normalized term related to diffusion of non-autonomous stochastic differential equation are obtained.Conclusions. Results of the paper can be used for further research on the asymptotic behavior of stochastic differential equation solutions, finding the stability condition of stochastic differential equation solution and ergodic type problems also.
Highlights
Asymptotic behavior at infinity of non-autonomous stochastic differential equation solutions is studied in the paper
find sufficient conditions for the strong law of large numbers for a random process which is a solution of non-autonomous stochastic differential equation
Basic results of the theory of stochastic differential equations related to stochastic integrals estimation
Summary
Asymptotic behavior at infinity of non-autonomous stochastic differential equation solutions is studied in the paper. The aim of the work is to find sufficient conditions for the strong law of large numbers for a random process which is a solution of non-autonomous stochastic differential equation. При дослідженні асимптотичної поведінки розв’язків стохастичних диференціальних рівнянь виникають задачі типу ПЗВЧ. У роботах [2, 3] досліджувалась асимптотична поведінка стохастичного диференціального рівняння із фазовими незалежними збуреннями, тобто dX (t ) g(X (t ))dt (t )dw(t ). Аналогічні задачі, але для так званого стохастичного диференціального рівняння з відокремлюваними змінними, досліджувались у роботах [4, 5]: dX (t ) g(X (t )) (t )dt (X (t )) (t )dw(t ). В усіх згаданих вище роботах властивості стохастичного диференціального рівняння визначалися властивостями розв’язку відповідної детермінованої задачі
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Research Bulletin of the National Technical University of Ukraine "Kyiv Politechnic Institute"
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
