Zhenting Hou 
Hailing Dong^{†} 
Peng Shi 
School of Mathematics Central South University Changsha 410075 Hunan China 
School of Mathematics Central South University Changsha 410075 Hunan China hailing_fly@mail.csu.edu.cn 
Faculty of Advanced Technology University of Glamorgan Pontypridd CF37 1DL UK 

Received March 17, 2007; revised August 6, 2007

Abstract
In this paper, finite phase semiMarkov processes are introduced. By introducing variables and a simple transformation, every finite phase semiMarkov process can be transformed to a finite Markov chain which is called its associated Markov chain. A consequence of this is that every phase semiMarkovian switching system may be equivalently expressed as its associated Markovian switching system. Existing results for Markovian switching systems may then be applied to analyze phase semiMarkovian switching systems. In the following, we obtain asymptotic stability for the distribution of nonlinear stochastic systems with semiMarkovian switching. The results can also be extended to general semiMarkovian switching systems. Finally, an example is given to illustrate the feasibility and effectiveness of the theoretical results obtained.
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2000 Mathematics Subject Classification:
primary 34A34; secondary 60K15

(Metadata: XML, RSS, BibTeX) 
MathSciNet:
MR2376??? 
^{†}indicates author for correspondence 
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