Necessary and sufficient conditions for mean square consensus under Markov switching topologies

2013 ◽  
Vol 44 (1) ◽  
pp. 178-186 ◽  
Author(s):  
Guoying Miao ◽  
Shengyuan Xu ◽  
Yun Zou
Keyword(s):  
Markov Switching ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Mean Square ◽  
Switching Topologies ◽  
Necessary And Sufficient ◽  
Mean Square Consensus

Necessary and sufficient conditions for ergodicity of CIR type SDEs with Markov switching

2019 ◽  
Vol 19 (03) ◽  
pp. 1950023 ◽  
Author(s):  
Zhenzhong Zhang ◽  
Hongqian Yang ◽  
Jinying Tong ◽  
Liangjian Hu
Keyword(s):  
Interest Rate ◽  
Markov Switching ◽  
Sufficient Conditions ◽  
Wasserstein Distance ◽  
Necessary And Sufficient Conditions ◽  
Exponential Rate ◽  
Transition Semigroup ◽  
Rate Model ◽  
Interest Rate Model ◽  
Necessary And Sufficient

In this paper, we consider the ergodicity and transience of the Cox–Ingersoll–Ross (CIR) interest rate model with Markov switching. Using the theory of [Formula: see text]-matrices, we give some necessary and sufficient conditions for ergodicity of the CIR interest rate model with Markov switching. Besides, we show that the transition semigroup converges to the stationary distribution at an exponential rate in the Wasserstein distance. Finally, two examples are presented to illustrate our theory.

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