Abstract
Continuous Markov chains in a random environment are modeled as a linear RODE on a probability simplex. The positivity of the solutions of such linear RODEs is established and the resulting linear random dynamical system is shown to be strongly contracting and to possess a random attractor consisting of singleton sets.
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Notes
- 1.
\(\mathbb {T}\) \(=\) \(\mathbb {Z}\) in the discrete-time case and \(\mathbb {R}\) in the continuous-time case.
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© 2017 Springer Nature Singapore Pte Ltd.
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Han, X., Kloeden, P.E. (2017). Random Markov Chains. In: Random Ordinary Differential Equations and Their Numerical Solution. Probability Theory and Stochastic Modelling, vol 85. Springer, Singapore. https://doi.org/10.1007/978-981-10-6265-0_18
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DOI: https://doi.org/10.1007/978-981-10-6265-0_18
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Publisher Name: Springer, Singapore
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Online ISBN: 978-981-10-6265-0
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