Stochastic Differential Equations With Markovian Switching

By Xuerong Mao, Chenggui Yuan. 2006

1,817 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/e66a2a3d16444170411178f7ea66bffaeec67c5a

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In Finance

1. George Yin
2. Xiaoyue Li
3. Jinghai Shao
4. Meng Liu
5. Chao Zhu
6. Xuerong Mao
7. Quanxin Zhu
8. Jianhai Bao

Citations in the corpus

• Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment (2016, background): “Then by the strong law of large numbers for martingales [9, 18], we have”
• Stochastic population dynamics under regime switching II (2007, background): “[3, 22]), we observe that A(i) = (aik)i))n×n has negative diagonal elements and non-negative off-diagonal elements, that is ajj(i) < 0, ajk(i) ≥ 0, 1 ≤ j, k ≤ n, j 6= k.”
• A survey on Markovian jump systems: Modeling and design (2015, background): “The stability analysis and stabilization problems for MJSs have been addressed in [17-29].”
• Stochastic Population Dynamics Driven by Levy Noise (2011, methodology): “functional Kolmogorov-type systems [11, 12]; hybrid competitive Lotka-Volterra models in [8, 13, 14, 15].”
• Persistence and extinction in stochastic non-autonomous logistic systems (2011, neutral): “[13,19,30]).”
• Stability analysis for stochastic hybrid systems: A survey (2014, background): “& Yin, 2007; Mao, 1999; Mao, Yin, & Yuan, 2007; Mao & Yuan, 2006; Pang, Deng, & Mao, 2008; Yin & Zhu, 2010; Yuan & Lygeros, 2005a,b; Yuan & Mao, 2003), impulsive switching diffusions (Yang, Li, & Chen, 2009), stochastic impulsive systems driven by renewal processes (Antunes, Hespanha, & Silvestre,…”
• Population dynamical behavior of a two-predator one-prey stochastic model with time delay (2017, background): “Model (2) is said to be stable in distribution ([34]) if there exists a unique probability measure ν such that for any N(θ) ∈ C([−τ̄ , 0], R(3) +), the transition probability p(t, φ, ·) of N(t) converges weakly to ν as t→ +∞.”
• Stabilisation of hybrid stochastic differential equations by feedback control based on discrete-time observations of state and mode (2017, background): “1 Introduction Mao [1] recently initiated the study of the mean-square exponential stabilisation of continuous-time hybrid stochastic differential equations (SDEs) (also known as SDEs with Markovian switching [2]) by feedback controls based on the discrete-time observations of the state.”
• Approximation of Invariant Measures for Regime-switching Diffusions (2014, background): “Since solving RSDPs is a challenging task, numerical schemes and/or approximation techniques have become one of the viable alternatives, where [14, 29] are concerned with finite–time (strong or weak) convergence while [11, 14] are devoted to long-time behavior of numerical schemes.”
• Certain properties related to well posedness of switching diffusions (2017, background): “Systematic treatments and comprehensive study of these stochastic processes can be found in [10] and [16].”
• New results on stability of singular stochastic Markov jump systems with state‐dependent noise (2015, methodology): “Proof By generalized Itô’s formula in [25] and Theorem 2 of [32], the aforementioned lemma can be verified.”