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
Structured robust stability and boundedness of nonlinear hybrid delay systems
TL;DR: Taking different structures in different modes into account, a new theory on the structured robust stability and boundedness for nonlinear hybrid stochastic differential delay equations (SDDEs) without the linear growth condition is developed.
Journal ArticleDOI
Synchronization of neutral complex dynamical networks with Markovian switching based on sampled-data controller
Xinghua Liu,Hongsheng Xi +1 more
TL;DR: The synchronization problem of a neutral complex dynamical network (NCDN) with distributed delay, Markovian jump parameters and partially unknown transition rates via sampled-data controller through Lyapunov-Krasovskii stability theory, integral matrix inequalities and reciprocally convex lemma is investigated.
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Stochastic stability criterion of neutral-type neural networks with additive time-varying delay and uncertain semi-Markov jump
TL;DR: By constructing an eligible stochastic Lyapunov–Krasovskii functional with considering more information about various time delays, uncertain semi-Markov jumping parameters, some stability criterions are derived via utilizing the improved inequality together with some integral inequalities.
Journal ArticleDOI
Preserving exponential mean-square stability in the simulation of hybrid stochastic differential equations
TL;DR: Euler–Maruyama and implicit theta-method discretisations are shown to capture exponential mean-square stability for all sufficiently small time-steps under appropriate conditions, and the decay rate, as measured by the second moment Lyapunov exponent, can be reproduced arbitrarily accurately.
Journal ArticleDOI
Stability of nonlinear regime-switching jump diffusion
Zhixin Yang,G. Yin +1 more
TL;DR: In this article, the authors focus on stability issues of switching jump diffusions and derive necessary conditions for exponential p -stability in the large and small scales, respectively, using the smooth-dependence on the initial data.
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.