IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v27y2025i3d10.1007_s11009-025-10189-z.html
   My bibliography  Save this article

Backward Non-Homogeneous Markov Systems: Weak Ergodicity

Author

Listed:
  • P.-C.G Vassiliou

    (Department of Mathematics, AUTH)

Abstract

The foundation of the novel stochastic process Backward Non-Homogeneous Markov system ( $$\mathcal {B}$$ B -NHMS) is provided in the present. This process is closely connected with the problem of tendency to consensus in an information exchanging operation. A problem which has attracted more than a few thousands of citations in the literature and where backward products of stochastic matrices appear. For forward NHMS with chronological order it is known that weak ergodicity does not necessarily imply strong ergodicity. In a basic Theorem it is proved that in $$\mathcal {B}$$ B -NHMS with chronological order weak ergodicity always imply strong ergodicity. Later sufficient and necessary conditions are provided for strong ergodicity of $$\mathcal {B}$$ B -NHMS to converge with geometrical rate uniformly. Next ergodicity of $$ \mathcal {B}$$ B -NHMS is studied when the input process is a non-homogeneous Poisson process. Finally an illustration of some of the main results are given for a manpower system with four grades.

Suggested Citation

  • P.-C.G Vassiliou, 2025. "Backward Non-Homogeneous Markov Systems: Weak Ergodicity," Methodology and Computing in Applied Probability, Springer, vol. 27(3), pages 1-23, September.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:3:d:10.1007_s11009-025-10189-z
    DOI: 10.1007/s11009-025-10189-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-025-10189-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-025-10189-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Esther Duflo & Emmanuel Saez, 2003. "The Role of Information and Social Interactions in Retirement Plan Decisions: Evidence from a Randomized Experiment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(3), pages 815-842.
    2. Cohen, Joel E. & Hajnal, John & Newman, Charles M., 1986. "Approaching consensus can be delicate when positions harden," Stochastic Processes and their Applications, Elsevier, vol. 22(2), pages 315-322, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tullio Jappelli, 2010. "Economic Literacy: An International Comparison," Economic Journal, Royal Economic Society, vol. 120(548), pages 429-451, November.
    2. Mitchell, O.S. & Piggott, J., 2016. "Workplace-Linked Pensions for an Aging Demographic," Handbook of the Economics of Population Aging, in: Piggott, John & Woodland, Alan (ed.), Handbook of the Economics of Population Aging, edition 1, volume 1, chapter 0, pages 865-904, Elsevier.
    3. Goda, Gopi Shah & Manchester, Colleen Flaherty & Sojourner, Aaron J., 2014. "What will my account really be worth? Experimental evidence on how retirement income projections affect saving," Journal of Public Economics, Elsevier, vol. 119(C), pages 80-92.
    4. Giulietti, Corrado & Vlassopoulos, Michael & Zenou, Yves, 2023. "When reality bites: Local deaths and vaccine take-up," European Economic Review, Elsevier, vol. 156(C).
    5. Fishman, Arthur & Fishman, Ram & Gneezy, Uri, 2019. "A tale of two food stands: Observational learning in the field," Journal of Economic Behavior & Organization, Elsevier, vol. 159(C), pages 101-108.
    6. Angrist, Josh & Lavy, Victor, 2002. "The Effect of High School Matriculation Awards: Evidence from Randomized Trials," CEPR Discussion Papers 3827, C.E.P.R. Discussion Papers.
    7. Adnan Q. Khan & Steven F. Lehrer, 2013. "The Impact of Social Networks on Labour Market Outcomes: New Evidence from Cape Breton," Canadian Public Policy, University of Toronto Press, vol. 39(s1), pages 1-24, May.
    8. Annette Alstadsæter & Wojciech Kopczuk & Kjetil Telle, 2019. "Social networks and tax avoidance: evidence from a well-defined Norwegian tax shelter," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 26(6), pages 1291-1328, December.
    9. Machikita, Tomohiro, 2006. "Are Job Networks Localized in a Developing Economy? Search Methods for Displaced Workers in Thailand," IDE Discussion Papers 84, Institute of Developing Economies, Japan External Trade Organization(JETRO).
    10. Silvia Jordan & Corinna Treisch, 2010. "The perception of tax concessions in retirement savings decisions," Qualitative Research in Financial Markets, Emerald Group Publishing Limited, vol. 2(3), pages 157-184, October.
    11. Carlos Santiago Guzm√°n Guti√©rrez, 2019. "Sistema Pensional Colombiano: implicaciones de la educaci√≥n financiera sobre las decisiones de traslado de los individuos," Documentos CEDE 17677, Universidad de los Andes, Facultad de Economía, CEDE.
    12. Bruno Crépon & Esther Duflo & Marc Gurgand & Roland Rathelot & Philippe Zamora, 2013. "Do Labor Market Policies have Displacement Effects? Evidence from a Clustered Randomized Experiment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 531-580.
    13. Ariel BenYishay & A. Mushfiq Mobarak, 2014. "Social Learning and Communication," NBER Working Papers 20139, National Bureau of Economic Research, Inc.
    14. Ingar Haaland & Christopher Roth & Johannes Wohlfart, 2023. "Designing Information Provision Experiments," Journal of Economic Literature, American Economic Association, vol. 61(1), pages 3-40, March.
    15. Bet Caeyers, 2014. "Peer effects in development programme awareness of vulnerable groups in rural Tanzania," CSAE Working Paper Series 2014-11, Centre for the Study of African Economies, University of Oxford.
    16. James Choi & David Laibson & Brigitte Madrain & Andrew Metrick, 2007. "Reinforcement Learning in Investment Behavior," Levine's Bibliography 122247000000001737, UCLA Department of Economics.
    17. Meier, Stephan & Sprenger, Charles D., 2013. "Discounting financial literacy: Time preferences and participation in financial education programs," Journal of Economic Behavior & Organization, Elsevier, vol. 95(C), pages 159-174.
    18. Kenneth T. Gillingham & Sébastien Houde & Arthur A. van Benthem, 2021. "Consumer Myopia in Vehicle Purchases: Evidence from a Natural Experiment," American Economic Journal: Economic Policy, American Economic Association, vol. 13(3), pages 207-238, August.
    19. Baylis, Kathy & Ham, Andres, 2015. "How important is spatial correlation in randomized controlled trials?," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205586, Agricultural and Applied Economics Association.
    20. Assar Lindbeck & Mårten Palme & Mats Persson, 2016. "Sickness Absence and Local Benefit Cultures," Scandinavian Journal of Economics, Wiley Blackwell, vol. 118(1), pages 49-78, January.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:27:y:2025:i:3:d:10.1007_s11009-025-10189-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.