Lyapunov Stability of the Generalized Stochastic Pantograph Equation
Joint Authors
Kadiev, Ramazan
Ponosov, Arcady
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-06-19
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
The purpose of the paper is to study stability properties of the generalized stochastic pantograph equation, the main feature of which is the presence of unbounded delay functions.
This makes the stability analysis rather different from the classical one.
Our approach consists in linking different kinds of stochastic Lyapunov stability to specially chosen functional spaces.
To prove stability, we check that the solutions of the equation belong to a suitable space of stochastic processes, instead of searching for an appropriate Lyapunov functional.
This gives us possibilities to study moment stability, stability with probability 1, and many other stability properties in an efficient way.
We show by examples how this approach works in practice, putting emphasis on delay-independent stability conditions for the generalized stochastic pantograph equation.
The framework can be applied to any stochastic functional differential equation with finite dimensional initial conditions.
American Psychological Association (APA)
Kadiev, Ramazan& Ponosov, Arcady. 2018. Lyapunov Stability of the Generalized Stochastic Pantograph Equation. Journal of Mathematics،Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1193585
Modern Language Association (MLA)
Kadiev, Ramazan& Ponosov, Arcady. Lyapunov Stability of the Generalized Stochastic Pantograph Equation. Journal of Mathematics No. 2018 (2018), pp.1-9.
https://search.emarefa.net/detail/BIM-1193585
American Medical Association (AMA)
Kadiev, Ramazan& Ponosov, Arcady. Lyapunov Stability of the Generalized Stochastic Pantograph Equation. Journal of Mathematics. 2018. Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1193585
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193585