Stability of stochastic differential equations with Markovian switching
TLDR
In this paper, the authors discuss the exponential stability of nonlinear stochastic differential equations with Markovian switching and show that the stability can be improved by using Markovians.About:
This article is published in Stochastic Processes and their Applications.The article was published on 1999-01-01 and is currently open access. It has received 714 citations till now. The article focuses on the topics: Stochastic partial differential equation & Stochastic differential equation.read more
Citations
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Journal ArticleDOI
Stability of a stochastic discrete SIS epidemic model with general nonlinear incidence rate
Maoxing Liu,Rong Yuan +1 more
TL;DR: In this article , the stability of a stochastic discrete SIS epidemic model with a general nonlinear incidence rate at the equilibrium was studied, and sufficient conditions for the stability at positive equilibrium and boundary equilibrium were obtained.
Journal ArticleDOI
Stability of a Non-Lipschitz Stochastic Riemann-Liouville Type Fractional Differential Equation Driven by Lévy Noise
Proceedings ArticleDOI
Stochastic Positivity and Stability Analysis for Discrete-Time Linear Systems
Ying Jin,Jinling Liang,Lan Wang +2 more
TL;DR: In this article, a new and novel definition is given to describe the positivity characteristic of certain systems in the sense of probability and certain nonnegativeness property is provided for the mathematical expectation of the solutions concerning the considered stochastic linear system.
Journal ArticleDOI
Practical φ 0 -stability of switched stochastic nonlinear systems and corresponding stochastic perturbation theory
TL;DR: In this article, the authors studied the practical φ 0 -stability in probability (Pφ 0 SiP) and practical ε −stability of pth mean of switched stochastic nonlinear systems with the comparison principle and the cone-valued Lyapunov function methods.
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L<sub>2</sub>-L∞ Filter Design With Adjustable Convergence Rate for Linear Stochastic Systems
TL;DR: In this article , a new criterion was proposed to make a more accurate judgment, which can not only guarantee the stability of the filtering error system with performance level but also can estimate the convergence speed of the filter.
References
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Book
Nonnegative Matrices in the Mathematical Sciences
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
BookDOI
Stochastic differential equations and applications
TL;DR: In this paper, the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form, are discussed, as well as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists.
Book
Applied Theory of Functional Differential Equations
TL;DR: In this paper, the authors present an overview of state estimates of stochastic systems with delay and their control for deterministic FEDs, including optimal control of Stochastic Delay Systems.