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Markov Chains

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Essentials of Stochastic Processes

Part of the book series: Springer Texts in Statistics ((STS))

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Abstract

The importance of Markov chains comes from two facts: (i) there are a large number of physical, biological, economic, and social phenomena that can be modeled in this way, and (ii) there is a well-developed theory that allows us to do computations. We begin with a famous example, then describe the property that is the defining feature of Markov chains

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References

  • Athreya, K.B. and Ney, P.E. (1972) Branching Processes. Springer-Verlag, New York

    Book  MATH  Google Scholar 

  • Geman, S. and Geman, D. (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration ofimages. IEEE Transactions on Pattern Analysis and Machine Intelligence. 6, 721–741

    Article  MATH  Google Scholar 

  • Gliovich, T., Vallone, R., and Tversky, A. (1985) The Hot Hand in Basketball: On the Misperception of Random Sequences. Cognitive Psychology. 17, 295–314

    Article  Google Scholar 

  • Hastings, W.K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109

    Article  MathSciNet  MATH  Google Scholar 

  • Kirkpatrick, S., Gelatt, Jr., C.D., and Vecchi, M.PP. (1983) Optimizing by simulated annealing. Science. 220, 671–680

    Article  MathSciNet  MATH  Google Scholar 

  • Tierney, L. (1994) Markov chains for exploring posterior distributions. Annals of Statistics. 22,, 1701–1762

    MathSciNet  MATH  Google Scholar 

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Durrett, R. (2016). Markov Chains. In: Essentials of Stochastic Processes. Springer Texts in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-45614-0_1

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