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Hybrid competitive Lotka–Volterra ecosystems with a hidden Markov chain 被引量:1
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作者 ky tran George Yin 《Journal of Control and Decision》 EI 2014年第1期51-74,共24页
This work concerns Lotka–Volterra models that are formulated using stochastic differential equations with regime-switching.Distinct from the existing formulations,the Markov chain that models random environments is u... This work concerns Lotka–Volterra models that are formulated using stochastic differential equations with regime-switching.Distinct from the existing formulations,the Markov chain that models random environments is unobservable.For such partially observed systems,we use Wonham’s filter to estimate the Markov chain from the observable evolution of the population,and convert the original system to a completely observable one.We then show that the positive solution of our model does not explode in finite time with probability 1.Several properties including stochastic boundedness,finite moments,sample path continuity and large-time asymptotic behaviour are also obtained.Moreover,stochastic permanence,extinction and feedback controls are also investigated. 展开更多
关键词 Lotka-Volterra model hidden Markov chain partially observed system
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Asymptotic Expansions for Solutions of Parabolic Systems Associated with Multi-scale Switching Diffusions
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作者 ky tran G.YIN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2017年第3期731-752,共22页
This work develops asymptotic expansions of systems of partial differential equations associated with multi-scale switching diffusions. The switching process is modeled by using an inhomogeneous continuous- time Marko... This work develops asymptotic expansions of systems of partial differential equations associated with multi-scale switching diffusions. The switching process is modeled by using an inhomogeneous continuous- time Markov chain. In the model, there are two small parameters ε and δ. The first one highlights the fast switching, whereas the other delineates the slow diffusion. Assuming that ε and δ are related in that ε = δγ, our results reveal that different values of γ lead to different behaviors of the underlying systems, resulting in different asymptotic expansions. Although our motivation comes from stochastic problems, the approach is mainly analytic and is constructive. The asymptotic series are rigorously justified with error bounds provided. An example is provided to demonstrate the results. 展开更多
关键词 asymptotic expansion multi-scale approach switching diffusion
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