Neutral Stochastic Differential Delay Equations with Markovian Switching

By V. Kolmanovskii, N. Koroleva, T. Maizenberg, Xuerong Mao, A. Matasov. 2003

151 citations recorded by the source corpus.

Abstract Neutral stochastic differential delay equations (NSDDEs) have recently been studied intensively (see Kolmanovskii, V.B. and Nosov, V.R., Stability and Periodic Modes of Control Systems with Aftereffect; Nauka: Moscow, 1981 and Mao X., Stochastic Differential Equations and Their Applications; Horwood Pub.: Chichester, 1997). Given that many systems are often subject to component failures or repairs, changing subsystem interconnections and abrupt environmental disturbances etc., the structure and parameters of underlying NSDDEs may change abruptly. One way to model such abrupt changes is to use the continuous‐time Markov chains. As a result, the underlying NSDDEs become NSDDEs with Markovian switching which are hybrid systems. So far little is known about the NSDDEs with Markovian switching and the aim of this paper is to close this gap. In this paper we will not only establish a fundamental theory for such systems but also discuss some important properties of the solutions e.g. boundedness and stability.

Subfields: Computer Networks and Communications, Finance, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/9c7d038320d923776510cc0f228985c7cf0bd95c

How researchers see this paper

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In Computer Networks and Communications

1. Peng Shi
2. W. Zheng
3. Yun Chen
4. Chenggui Yuan
5. Cheng-Chew Lim
6. Huabin Chen
7. Xuerong Mao
8. Shengyuan Xu

In Finance

1. Xuerong Mao
2. Chenggui Yuan
3. Fuke Wu
4. Peng Shi
5. Huabin Chen
6. W. Zheng
7. Yun Chen
8. George Yin

In Public Health, Environmental and Occupational Health

1. Chenggui Yuan
2. Xuerong Mao
3. W. Zheng
4. Ke Wang
5. Meng Liu
6. Jianhai Bao

Citations in the corpus

• Exponential stability of the exact and numerical solutions for neutral stochastic delay differential equations (2016, background): “2 in [8], the exponent c 1⁄4 c ^ 1 2s logð1 jÞ is clearly lager than that of Theorem 3.”
• Stability of neutral stochastic switched time delay systems: An average dwell time approach (2017, methodology): “Although some methods, such as Razumikhin-type theorem [3], Lyapunov-type theorem [4, 5, 10, 11], LMI approach [6–9], and integral inequality [12, 13] have been used to consider the exponential stability in moment for neutral stochastic delay differential systems, these proposed approaches are only ”
• Exponential H ∞  filtering for stochastic Markovian jump systems with time delays (2014, methodology): “t/ whose structure and parameters may experience abrupt changes that can be modeled by the continuous-time Markov chains [29].”
• Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching (2008, background): “(1.3) In [12], the existence and uniqueness of the solution to Eq.”