Abstract
This paper is devoted to presenting an averaging principle for stochastic pantograph equations. Under suitable non-Lipschitz conditions, the solutions to stochastic pantograph equations can be approximated by solutions to averaged stochastic systems in the mean-square sense and probability. At last, an example is given to demonstrate the feasibility of obtained results. Moreover, our results have generalized significantly some previous ones.
Highlights
Pantograph equations [1] are a kind of equations with unbounded delay, and they were used in describing the various phenomena like biology, electrodynamics, economy, and some other nonlinear dynamical systems [2,3,4]
The averaging principle as a powerful method has been largely applied in stochastic differential systems, and its main role is to strike a balance between complex models that are more realistic and simpler models that are more amenable to analysis and simulation
Referring to the averaging principle, we are indispensable to recall some excellent articles [9,10,11,12,13], which have discussed the corresponding solutions to stochastic differential equations by the averaging principle
Summary
Pantograph equations [1] are a kind of equations with unbounded delay, and they were used in describing the various phenomena like biology, electrodynamics, economy, and some other nonlinear dynamical systems [2,3,4]. To the best of authors’ knowledge, there is no paper which has considered the approximation theorem as an averaging principle for stochastic pantograph equations. (i) We first attempt to investigate the property of solutions for a class of stochastic pantograph equations by the averaging principle under the non-Lipschitz conditions. Erefore, in this paper, we consider a kind of delay stochastic differential equations with a linear delay τ(t) θt with 0 < θ < 1.
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 callDisclaimer: 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.
