Proceedings Article10.1109/CDC.2008.4739497
On hybrid diffusions
Chao Zhu,Gang George Yin +1 more
- 01 Dec 2008
- pp 1507-1512
TL;DR: Using Liapunov functions, necessary and sufficient conditions for weak stability are derived and ergodicity of weakly stable regime-switching diffusions is obtained by constructing cycles using the associated discrete-time Markov chains.
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Abstract: For the pressing needs in control and optimization using hybrid systems, this work focuses on weak stochastic stability and ergodicity of regime-switching diffusions. Using Liapunov functions, we derive necessary and sufficient conditions for weak stability. Then, ergodicity of weakly stable regime-switching diffusions is obtained by constructing cycles using the associated discrete-time Markov chains.
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Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
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TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
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TL;DR: In this paper, a class of partial differential equations that generalize and are represented by Laplace's equation was studied. And the authors used the notation D i u, D ij u for partial derivatives with respect to x i and x i, x j and the summation convention on repeated indices.
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Jean Jacod,Albert N. Shiryaev +1 more
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TL;DR: In this article, the General Theory of Stochastic Processes, Semimartingales, and Stochastically Integrals is discussed and the convergence of Processes with Independent Increments is discussed.
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TL;DR: The One-Dimensional Maximum Principle (MDP) as mentioned in this paper is a generalization of the one-dimensional maximum principle (OMP) for the construction of hyperbolic equations.
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TL;DR: In this article, the authors define the boundedness in probability and stability of Stochastic Processes Defined by Differential Equations (SDEs) defined by Markov Processes.
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