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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Original article: Invariant distribution of stochastic Gompertz equation under regime switching
TL;DR: It is shown that this model is asymptotically stable in distribution and that it displays an invariant probability distribution under certain conditions as well as the trajectories and the limits probability distribution of the solution with the method of Monte Carlo stochastic simulation.
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${ {\mathcal H} }_{\infty }$ couple-group consensus of stochastic multi-agent systems with fixed and Markovian switching communication topologies
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A note on sufficient conditions for asymptotic stability in distribution of stochastic differential equations with Markovian switching
TL;DR: In this article, the authors improved the results on stability in distribution of nonlinear stochastic differential equations in Yuan and Mao (2003) by weakening the conditions for the stability of distribution given in that paper.
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Stochastic properties of tumor growth driven by white lévy noise
TL;DR: In this paper, the dynamics of tumor growth model driven by Levy noise terms are investigated for α = 2 and β = 0, the process driven by white Levy noise approach to the standard Gaussian white noise can be viewed in the analysis of the steady-state probability distribution and the mean first-passage time.
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State-feedback stabilization for stochastic high-order nonlinear systems with Markovian switching
Wuquan Li,Hui Wang,Xiaohua Liu +2 more
TL;DR: In this paper, a state-feedback controller is constructed to ensure that the closed-loop system has a unique solution and the solution of the closedloop systems is almost surely asymptotically stable.
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.