Journal of Systems Science and Complexity

, Volume 30, Issue 5, pp 999–1011 | Cite as

Stochastic systems arising from Markov modulated empirical measures

  • Gang YinEmail author
  • Trang Bui


This work is devoted to stochastic systems arising from empirical measures of random sequences (termed primary sequences) that are modulated by another Markov chain. The Markov chain is used to model random discrete events that are not represented in the primary sequences. One novel feature is that in lieu of the usual scaling in empirical measure sequences, the authors consider scaling in both space and time, which leads to new limit results. Under broad conditions, it is shown that a scaled sequence of the empirical measure converges weakly to a number of Brownian bridges modulated by a continuous-time Markov chain. Ramifications and special cases are also considered.


Brownian bridge limit empirical measure multi-scale modeling regime-switching model weak convergence 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsWayne State UniversityDetroitUSA

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