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Monotone matrices and monotone Markov processes

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  • Keilson, Julian
  • Kester, Adri

Abstract

A stochastic matrix is "monotone" [4] if its row-vectors are stochastically increasing. Closure properties, characterizations and the availability of a second maximal eigenvalue are developed. Such monotonicity is present in a variety of processes in discrete and continous time. In particular, birth-death processes are monotone. Conditions for the sequential monotonicity of a process are given and related inequalities presented.

Suggested Citation

  • Keilson, Julian & Kester, Adri, 1977. "Monotone matrices and monotone Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 5(3), pages 231-241, July.
    • Handle: RePEc:eee:spapps:v:5:y:1977:i:3:p:231-241
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    1. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    2. Valentino Dardanoni & Mario Fiorini & Antonio Forcina, 2012. "Stochastic monotonicity in intergenerational mobility tables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(1), pages 85-107, January.
    3. Daly, David & Buchholz, Peter & Sanders, William H., 2007. "A preorder relation for Markov reward processes," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1148-1157, June.
    4. Özkan, Can & Karaesmen, Fikri & Özekici, Süleyman, 2013. "Structural properties of Markov modulated revenue management problems," European Journal of Operational Research, Elsevier, vol. 225(2), pages 324-331.
    5. Roland Benabou & Efe A. Ok, 2001. "Social Mobility and the Demand for Redistribution: The Poum Hypothesis," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(2), pages 447-487.
    6. Christopher A. Hennessy & Ilya A. Strebulaev, 2020. "Beyond Random Assignment: Credible Inference and Extrapolation in Dynamic Economies," Journal of Finance, American Finance Association, vol. 75(2), pages 825-866, April.
    7. Harkins, Andrew, 2020. "Network Comparative Statics," The Warwick Economics Research Paper Series (TWERPS) 1306, University of Warwick, Department of Economics.
    8. Harkins, Andrew, 2020. "Network Comparative Statics," CRETA Online Discussion Paper Series 64, Centre for Research in Economic Theory and its Applications CRETA.
    9. Roland Benabou & Efe A. Ok, 2000. "Mobility as Progressivity: Ranking Income Processes According to Equality of Opportunity," Working Papers 150, Princeton University, School of Public and International Affairs, Discussion Papers in Economics.
    10. Ravi Kumar & Mark E. Lewis & Huseyin Topaloglu, 2013. "Dynamic service rate control for a single‐server queue with Markov‐modulated arrivals," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 661-677, December.
    11. Nico M. van Dijk & Masakiyo Miyazawa, 2004. "Error Bounds for Perturbing Nonexponential Queues," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 525-558, August.
    12. Jing‐Sheng Song & Paul H. Zipkin, 2012. "Newsvendor problems with sequentially revealed demand information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(8), pages 601-612, December.
    13. Kuber, Madhuri & Dharmadhikari, Avinash, 1996. "Association in time of a finite semi-Markov process," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 125-133, February.
    14. repec:pri:wwseco:dp211 is not listed on IDEAS
    15. Jie-Ming Wang, 2013. "Stochastic Comparison for Lévy-Type Processes," Journal of Theoretical Probability, Springer, vol. 26(4), pages 997-1019, December.
    16. Satya R. Chakravarty & Nachiketa Chattopadhyay & Liu Qingbin, 2015. "Vulnerability Orderings for Expected Poverty Indices," The Japanese Economic Review, Japanese Economic Association, vol. 66(3), pages 300-310, September.
    17. Danny Ben‐Shahar & Eyal Sulganik, 2008. "Partial Ordering of Unpredictable Mobility with Welfare Implications," Economica, London School of Economics and Political Science, vol. 75(299), pages 592-604, August.
    18. Pekergin, Nihal & Dayar, Tugrul & Alparslan, Denizhan N., 2005. "Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering," European Journal of Operational Research, Elsevier, vol. 165(3), pages 810-825, September.

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