Stochastic differential delay equations with Markovian switching

By Xuerong Maoy, A. B. Piunovskiy. 2000

243 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/8f602cfc520e1761280f4e2d2a281fc137275030

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. James Lam
2. Shengyuan Xu
3. Peng Shi
4. Huijun Gao
5. Chenggui Yuan
6. Fanbiao Li
7. Kai Liu
8. Xuerong Mao

In Control and Systems Engineering

1. James Lam
2. Peng Shi
3. Huijun Gao
4. Shengyuan Xu
5. Fanbiao Li
6. Hamid Reza Karimi
7. Xuerong Mao
8. Ligang Wu

In Finance

1. Xuerong Mao
2. Chenggui Yuan
3. Jiaowan Luo
4. Huijun Gao
5. Shengyuan Xu
6. James Lam
7. Peng Shi
8. Kai Liu

Citations in the corpus

• Razumikhin method and exponential stability of hybrid stochastic delay interval systems (2006, background): “[15] investigated the stability of a nonlinear stochastic differential delay equation with Markovian switching.”
• Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps (2008, background): “[15,16] considered asymptotic and exponential stability of the following nonlinear stochastic delay differential equations with Markovian switching: dx(t) = f (x(t), x(t − τ), t, r(t))dt + g(x(t), x(t − τ), t, r(t))dw(t) where τ > 0 is a constant.”
• Neutral Stochastic Differential Delay Equations with Markovian Switching (2003, background): “[17,25]), there exists a unique global solution xk(t) on t ∈ [0, τ ] to”
• Asymptotic stability in distribution of stochastic differential equations with Markovian switching (2003, methodology): “…(1.2) Shaikhet (1996) took the time delay into account and considered the stability of a semi-linear stochastic di#erential delay equation with Markovian switching, while Mao et al. (2000) investigated the stability of a nonlinear stochastic di#erential delay equation with Markovian switching.”
• Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching (2008, background): “[17,25]), there exists a unique global solution xk(t) on t ∈ [0, τ ] to”
• Stability analysis for stochastic hybrid systems: A survey (2014, unknown): “Matasov, & Piunovskiy, 2000; Mao & Shaikhet, 2000; Peng & Zhang, 2010; Wang, Qiao, & Burnham, 2002; Xia, Boukas, Shi, & Zhang, 2009; Yang, Xu, & Xiang, 2006; Yuan & Mao, 2004; Yue, Fang, & Won, 2003; Yue & Han, 2005; Yue & Won, 2001).”
• A survey on Markovian jump systems: Modeling and design (2015, background): “Under these conditions, (3) has a unique solution; see [34] for more details.”