Statistical Inference for Stochastic Processes

, Volume 18, Issue 3, pp 293–313 | Cite as

Stability of the filter with Poisson observations

  • Zhiqiang Li
  • Jie XiongEmail author


The short interest rate process is modeled by a diffusion process \(X(t)\). With the counting process observations, a filtering problem is formulated and its exponential stability is derived when the process \(X(t)\) is asymptotically stationary.


Diffusion process Truncated filter Stability 

Mathematics Subject Classification

Primary 93E11 Secondary: 60J25 62M20 



This research supported partially by FDCT 076/2012/A3. The authors would like to thank the anonymous reviewer for the constructive suggestions and comments which improved this paper substantially.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TennesseeKnoxvilleUSA
  2. 2.Department of Mathematics, Faculty of Science and TechnologyUniversity of MacauTaipaMacau, China

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