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Hidden Markov Models in Finance pp 101–119Cite as

Filtering of Hidden Weak Markov Chain -Discrete Range Observations

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Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 104))

Summary

In this paper we consider a hidden discrete time finite state process X whose behavior at the present time t depends on its behavior at the previous k time steps, which is a generalization of the usual hidden finite state Markov chain, in which k equals to one. We consider the case when the range space of our observations is finite. We present filtering equations for certain functionals of the chain and perform related error analysis.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Northern Iowa, Cedar Falls, IA, 50614-0506, USA

    Shangzhen Luo

  2. Department of Mathematics, University of Missouri, Columbia, Missouri, 65211, USA

    Allanus H. Tsoi

Authors
  1. Shangzhen Luo
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  2. Allanus H. Tsoi
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Corresponding author

Correspondence to Shangzhen Luo .

Editor information

Editors and Affiliations

  1. University of Western Ontario, London, Canada

    Rogemar S. Mamon

  2. University of Calgary, Calgary, Canada

    Robert J. Elliott

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© 2007 Springer Science+Business Media, LLC

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Luo, S., Tsoi, A.H. (2007). Filtering of Hidden Weak Markov Chain -Discrete Range Observations. In: Mamon, R.S., Elliott, R.J. (eds) Hidden Markov Models in Finance. International Series in Operations Research & Management Science, vol 104. Springer, Boston, MA. https://doi.org/10.1007/0-387-71163-5_7

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