IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v11y2009i4d10.1007_s11009-008-9074-6.html
   My bibliography  Save this article

On the Distributions of the State Sizes of Closed Continuous Time Homogeneous Markov Systems

Author

Listed:
  • G. Vasiliadis

    (Aristotle University of Thessaloniki)

  • G. Tsaklidis

    (Aristotle University of Thessaloniki)

Abstract

The evolution of the state sizes of a closed continuous-time homogeneous Markov system is determined by the convolution of multinomial distributions expressing the number of transitions between the states of the system. In order to investigate the distributions of the state sizes, we provide the computation of their moments, at any time point, via a recursive formula concerning the derivative of the moments. The basic result is given by means of a new vector product which is similar to the Kronecker product. Finally, a formula for the computation of the state sizes distributions is given.

Suggested Citation

  • G. Vasiliadis & G. Tsaklidis, 2009. "On the Distributions of the State Sizes of Closed Continuous Time Homogeneous Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 561-582, December.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:4:d:10.1007_s11009-008-9074-6
    DOI: 10.1007/s11009-008-9074-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-008-9074-6
    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/s11009-008-9074-6?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 search for a different version of it.

    References listed on IDEAS

    as
    1. P.‐C. G. Vassiliou, 1997. "The evolution of the theory of non‐homogeneous Markov systems," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 13(3‐4), pages 159-176, September.
    2. G. J. Taylor & S. I. McClean & P. H. Millard, 2000. "Stochastic models of geriatric patient bed occupancy behaviour," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 163(1), pages 39-48.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. P. -C. G. Vassiliou, 2022. "Limiting Distributions of a Non-Homogeneous Markov System in a Stochastic Environment in Continuous Time," Mathematics, MDPI, vol. 10(8), pages 1-16, April.
    2. George Vasiliadis, 2012. "On the Distributions of the State Sizes of the Continuous Time Homogeneous Markov System with Finite State Capacities," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 863-882, September.
    3. Rodi Lykou & George Tsaklidis, 2021. "Particle Filtering: A Priori Estimation of Observational Errors of a State-Space Model with Linear Observation Equation," Mathematics, MDPI, vol. 9(12), pages 1-16, June.

    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. George Vasiliadis, 2012. "On the Distributions of the State Sizes of the Continuous Time Homogeneous Markov System with Finite State Capacities," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 863-882, September.
    2. P.-C. G. Vassiliou, 2020. "Laws of Large Numbers for Non-Homogeneous Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1631-1658, December.
    3. P.-C.G. Vassiliou, 2021. "Non-Homogeneous Markov Set Systems," Mathematics, MDPI, vol. 9(5), pages 1-25, February.
    4. G. Vasiliadis & G. Tsaklidis, 2008. "On the Distributions of the State Sizes of Discrete Time Homogeneous Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 55-71, March.
    5. Xiang Zhong & Jie Song & Jingshan Li & Susan M. Ertl & Lauren Fiedler, 2016. "Design and analysis of gastroenterology (GI) clinic in Digestive Health Center of University of Wisconsin Health," Flexible Services and Manufacturing Journal, Springer, vol. 28(1), pages 90-119, June.
    6. S McClean & P Millard, 2007. "Where to treat the older patient? Can Markov models help us better understand the relationship between hospital and community care?," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(2), pages 255-261, February.
    7. Andreas C. Georgiou & Alexandra Papadopoulou & Pavlos Kolias & Haris Palikrousis & Evanthia Farmakioti, 2021. "On State Occupancies, First Passage Times and Duration in Non-Homogeneous Semi-Markov Chains," Mathematics, MDPI, vol. 9(15), pages 1-17, July.
    8. repec:dgr:rugsom:02a63 is not listed on IDEAS
    9. Broyles, James R. & Cochran, Jeffery K. & Montgomery, Douglas C., 2010. "A statistical Markov chain approximation of transient hospital inpatient inventory," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1645-1657, December.
    10. P.-C. G. Vassiliou & T. P. Moysiadis, 2010. "$\boldsymbol{\mathcal{G}-}$ Inhomogeneous Markov Systems of High Order," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 271-292, June.
    11. McGrory, C.A. & Pettitt, A.N. & Faddy, M.J., 2009. "A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4311-4321, October.
    12. R. Bekker & A. Bruin, 2010. "Time-dependent analysis for refused admissions in clinical wards," Annals of Operations Research, Springer, vol. 178(1), pages 45-65, July.
    13. Gang Du & Xi Liang & Chuanwang Sun, 2017. "Scheduling Optimization of Home Health Care Service Considering Patients’ Priorities and Time Windows," Sustainability, MDPI, vol. 9(2), pages 1-22, February.
    14. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović & Izack Cohen, 2020. "Bed Blocking in Hospitals Due to Scarce Capacity in Geriatric Institutions—Cost Minimization via Fluid Models," Manufacturing & Service Operations Management, INFORMS, vol. 22(2), pages 396-411, March.
    15. P. -C. G. Vassiliou, 2022. "Limiting Distributions of a Non-Homogeneous Markov System in a Stochastic Environment in Continuous Time," Mathematics, MDPI, vol. 10(8), pages 1-16, April.
    16. Akkerman, Renzo & Knip, Marrig, 2002. "Reallocation of beds to reduce waiting time for cardiac surgery," Research Report 02A63, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    17. Xiang Zhong & Peter Hoonakker & Philip A. Bain & Albert J. Musa & Jingshan Li, 2018. "The impact of e-visits on patient access to primary care," Health Care Management Science, Springer, vol. 21(4), pages 475-491, December.
    18. P.-C.G. Vassiliou & Andreas C. Georgiou, 2021. "Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields," Mathematics, MDPI, vol. 9(19), pages 1-6, October.
    19. P. -C. G. Vassiliou, 2020. "Rate of Convergence and Periodicity of the Expected Population Structure of Markov Systems that Live in a General State Space," Mathematics, MDPI, vol. 8(6), pages 1-23, June.

    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:11:y:2009:i:4:d:10.1007_s11009-008-9074-6. 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.