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A Note on Independence Copula for Conditional Markov Chains

  • Tomasz R. BieleckiEmail author
  • Jacek Jakubowski
  • Mariusz Niewęgłowski
Chapter
Part of the Fields Institute Communications book series (FIC, volume 79)

Abstract

Given a family (Y k ,  k = 1, 2, , N) of conditional Markov chains, we construct a conditional Markov chain X = (X 1, , X N ) such that X k , k = 1, 2, , N, are conditional Markov chains, which are conditionally independent given the information contained in some filtration \(\mathbb{F}\), and such that for each k the conditional law of X k coincides with the conditional law of Y k . This is a new result that can be used to model different phenomena such as the gating behavior of multiple ion channels in a membrane patch, or credit ratings migrations.

Notes

Acknowledgements

We thank the referees and the editors for valuable comments and suggestions, which we used revising the original version of this note.

Research of T.R. Bielecki was partially supported by NSF grant DMS-1211256.

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Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  • Tomasz R. Bielecki
    • 1
    Email author
  • Jacek Jakubowski
    • 2
    • 3
  • Mariusz Niewęgłowski
    • 3
  1. 1.Department of Applied MathematicsIllinois Institute of TechnologyChicagoUSA
  2. 2.Institute of MathematicsUniversity of WarsawWarszawaPoland
  3. 3.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarszawaPoland

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