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A formula for the Perron vector of astochastic matrix

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The paper suggests a new linear-algebraic proof of a formula for the Perron vector (stationary distribution) of a stochastic matrix, known in the theory of Markov chains. Bibliography: 5 titles.

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References

  1. V. I. Romanovsky, Discrete Markov Chains [in Russian], Gostekhizdat, Moscow (1949).

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  2. F. R. Gantmakher, The Theory of Matrices [in Russian], Nauka, Moscow (1967).

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  3. P. Lanaster, Matrix Theory [Russian translation], Nauka, Moscow (1978).

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  4. A. N. Shiryaev, Probability-1, Probability-2, MTsNMO, Moscow (2004).

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  5. R. A. Horn and C. R. Johnson, Matrix Analysis [Russian translation], Mir, Moscow (1989).

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Authors and Affiliations

  1. Kazan’ State University Kazan’, Kazan’, Russia

    Yu. A. Al’pin

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  1. Yu. A. Al’pin
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Correspondence to Yu. A. Al’pin.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 367, 2009, pp. 5–8.

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Al’pin, Y.A. A formula for the Perron vector of astochastic matrix. J Math Sci 165, 499–500 (2010). https://doi.org/10.1007/s10958-010-9818-z

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  • DOI: https://doi.org/10.1007/s10958-010-9818-z

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