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On a New Class of Regular Doubly Stochastic Processes

Received: 17 March 2017     Accepted: 29 March 2017     Published: 25 May 2017
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Abstract

In this article, we show that the well-known Helmert matrix has strong relationship with stochastic matrices in modern probability theory. In fact, we show that we can construct some stochastic matrices by the Helmert matrix. Hence, we introduce a new class of regular and doubly stochastic matrices by use of the Helmert matrix and a special diagonal matrix that is defined in this article. Afterwards, we obtain the stationary distribution for this new class of stochastic matrices.

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 3)
DOI 10.11648/j.ajtas.20170603.14
Page(s) 156-160
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Helmert Matrix, Stochastic Matrix, Markov Chain, Transition Probability, Stationary Distribution, Regular Chain, Ergodic Chain

References
[1] B. R. Clarke. Linear Models: The Theory and Application of Analysis of variance. Wiley, 2008.
[2] J. E. Gentie, Numerical Linear Algebra for Application in Statistics, springer, 1998.
[3] A. Kehagias, Approximation of stochastic processes by hidden Markov models, U.M.I, 1992.
[4] H. O. Lancaster. The Helmert Matrices. The American Mathematical Monthly, 72(1965), no. 1, 4-12.
[5] E. Parzen, Stochastic Processes, San Francisco: Holden-Day, Inc., 1962.
[6] P. Perkins, “A theorem on regular matrices”. Pacific J. Math. 11 (1961), no. 4, 1529-1533.
[7] Ch. M. Grinstead, J. L. Snell, Introduction to Probability, American Mathematical Society, 1997.
[8] G. A. F. seber, A Matrix Handbook for Statistician, Wiley, 2007.
[9] S. M. Roos, A first cours in probability, 6th ed, Pearson Prentice Hall, 2002.
[10] S. M. Ross, Introduction to Probability Models. 7thth ed. San Diego, colif: Academic Press, Inc., 2000.
[11] S. M. Ross, Stochastic Processes. 2thndth ed. New York: john wiley & Sons, Inc., 1996.
[12] X. Zhan, Matrix Theory, Graduate studies in mathematics, volume 147, American Mathematical Society, 2013.
Cite This Article
  • APA Style

    Reza Farhadian, Nader Asadian. (2017). On a New Class of Regular Doubly Stochastic Processes. American Journal of Theoretical and Applied Statistics, 6(3), 156-160. https://doi.org/10.11648/j.ajtas.20170603.14

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    ACS Style

    Reza Farhadian; Nader Asadian. On a New Class of Regular Doubly Stochastic Processes. Am. J. Theor. Appl. Stat. 2017, 6(3), 156-160. doi: 10.11648/j.ajtas.20170603.14

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    AMA Style

    Reza Farhadian, Nader Asadian. On a New Class of Regular Doubly Stochastic Processes. Am J Theor Appl Stat. 2017;6(3):156-160. doi: 10.11648/j.ajtas.20170603.14

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  • @article{10.11648/j.ajtas.20170603.14,
      author = {Reza Farhadian and Nader Asadian},
      title = {On a New Class of Regular Doubly Stochastic Processes},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {6},
      number = {3},
      pages = {156-160},
      doi = {10.11648/j.ajtas.20170603.14},
      url = {https://doi.org/10.11648/j.ajtas.20170603.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170603.14},
      abstract = {In this article, we show that the well-known Helmert matrix has strong relationship with stochastic matrices in modern probability theory. In fact, we show that we can construct some stochastic matrices by the Helmert matrix. Hence, we introduce a new class of regular and doubly stochastic matrices by use of the Helmert matrix and a special diagonal matrix that is defined in this article. Afterwards, we obtain the stationary distribution for this new class of stochastic matrices.},
     year = {2017}
    }
    

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    T1  - On a New Class of Regular Doubly Stochastic Processes
    AU  - Reza Farhadian
    AU  - Nader Asadian
    Y1  - 2017/05/25
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ajtas.20170603.14
    DO  - 10.11648/j.ajtas.20170603.14
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
    SP  - 156
    EP  - 160
    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ajtas.20170603.14
    AB  - In this article, we show that the well-known Helmert matrix has strong relationship with stochastic matrices in modern probability theory. In fact, we show that we can construct some stochastic matrices by the Helmert matrix. Hence, we introduce a new class of regular and doubly stochastic matrices by use of the Helmert matrix and a special diagonal matrix that is defined in this article. Afterwards, we obtain the stationary distribution for this new class of stochastic matrices.
    VL  - 6
    IS  - 3
    ER  - 

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Author Information
  • Department of Mathematics and Statistics, Lorestan University, Khorramabad, Iran

  • Department of Mathematics and Statistics, Lorestan University, Khorramabad, Iran

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