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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Asymptotic expansions and stability of hybrid systems with two-time scales
TL;DR: The Autobiographical Statement as mentioned in this paper is a collection of essays written by the author of the book "Autobiography of a man: A Personal Essay" (1998).
Proceedings ArticleDOI
Exponential Stabilization of Time-Delayed Systems with Markovian Jumping
TL;DR: In this article, the stability and stabilization criteria for stochastic Markov jump systems are formulated in the form of linear matrix inequalities, and two numerical examples are exploited to illustrate the validity of the developed techniques.
Proceedings ArticleDOI
On hybrid diffusions
Chao Zhu,Gang George Yin +1 more
TL;DR: Using Liapunov functions, necessary and sufficient conditions for weak stability are derived and ergodicity of weakly stable regime-switching diffusions is obtained by constructing cycles using the associated discrete-time Markov chains.
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Analysis of a Bailey–Dietz model for vector-borne disease under regime switching
Jiang Xu,Tao Chen,Xiangdan Wen +2 more
TL;DR: In this paper, a stochastic Bailey-Dietz model with standard incidence under Markovian switching is proposed to study the spread of the vector-borne disease, and sufficient criteria for persistence in the mean of the disease are derived.
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Practical Stability of Large-Scale Stochastic Markovian Jump Systems with Time-Delays
Ping Zhao,Yan Zhao +1 more
TL;DR: The notions of the (strongly) practical stability in probability and in the pth mean are introduced for some large-scale stochastic systems with Markovian jump parameters and time-varying delays by using the comparison principle and Lyapunov function methods.
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.