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Tail of the stationary solution of the stochastic equation Yn+1=anYn+bn with Markovian coefficients

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  • de Saporta, BenoI^te

Abstract

In this paper, we deal with the real stochastic difference equation , where the sequence (an) is a finite state space Markov chain. By means of the renewal theory, we give a precise description of the situation where the tail of its stationary solution exhibits power law behavior.

Suggested Citation

  • de Saporta, BenoI^te, 2005. "Tail of the stationary solution of the stochastic equation Yn+1=anYn+bn with Markovian coefficients," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1954-1978, December.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:12:p:1954-1978
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    Cited by:

    1. Jess Benhabib & Alberto Bisin & Mi Luo, 2019. "Wealth Distribution and Social Mobility in the US: A Quantitative Approach," American Economic Review, American Economic Association, vol. 109(5), pages 1623-1647, May.
    2. Dave, Chetan & Malik, Samreen, 2017. "A tale of fat tails," European Economic Review, Elsevier, vol. 100(C), pages 293-317.
    3. Predrag R. Jelenković & Jian Tan, 2010. "Modulated Branching Processes, Origins of Power Laws, and Queueing Duality," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 807-829, November.
    4. Jess Benhabib & Alberto Bisin & Shenghao Zhu, 2011. "The Distribution of Wealth and Fiscal Policy in Economies With Finitely Lived Agents," Econometrica, Econometric Society, vol. 79(1), pages 123-157, January.
    5. Brendan K. Beare & Alexis Akira Toda, 2022. "Determination of Pareto Exponents in Economic Models Driven by Markov Multiplicative Processes," Econometrica, Econometric Society, vol. 90(4), pages 1811-1833, July.
    6. Cline, Daren B.H., 2007. "Regular variation of order 1 nonlinear AR-ARCH models," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 840-861, July.
    7. Benhabib, Jess & Bisin, Alberto & Zhu, Shenghao, 2015. "The wealth distribution in Bewley economies with capital income risk," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 489-515.
    8. Blanchet, Jose & Lam, Henry & Zwart, Bert, 2012. "Efficient rare-event simulation for perpetuities," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3361-3392.
    9. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    10. Cozzi, Guido & Mantovan, Noemi, 2021. "To get Rich is Glorious, but only if Fairly," MPRA Paper 107305, University Library of Munich, Germany.
    11. Jess Benhabib & Chetan Dave, 2014. "Learning, Large Deviations and Rare Events," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(3), pages 367-382, July.
    12. Stelzer, Robert, 2008. "Multivariate Markov-switching ARMA processes with regularly varying noise," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1177-1190, July.
    13. Christian Pietro & Marco M. Sorge, 2018. "Stochastic dominance and thick-tailed wealth distributions," Journal of Economics, Springer, vol. 123(2), pages 141-159, March.
    14. Sabiou Inoua, 2015. "The Intrinsic Instability of Financial Markets," Papers 1508.02203, arXiv.org.

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