IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v32y2019i3d10.1007_s10959-018-0835-z.html
   My bibliography  Save this article

On Distributions of Certain State-Dependent Fractional Point Processes

Author

Listed:
  • K. K. Kataria

    (Indian Institute of Technology Bombay)

  • P. Vellaisamy

    (Indian Institute of Technology Bombay)

Abstract

We obtain the explicit expressions for the state probabilities of various state-dependent versions of fractional point processes. The inversion of the Laplace transforms of the state probabilities of such processes is rather cumbersome and involved. We employ the Adomian decomposition method to solve the difference-differential equations governing the state probabilities of these state-dependent processes. The distributions of some convolutions of the Mittag-Leffler random variables are derived as special cases of the obtained results.

Suggested Citation

  • K. K. Kataria & P. Vellaisamy, 2019. "On Distributions of Certain State-Dependent Fractional Point Processes," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1554-1580, September.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:3:d:10.1007_s10959-018-0835-z
    DOI: 10.1007/s10959-018-0835-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-018-0835-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/s10959-018-0835-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 search for a different version of it.

    References listed on IDEAS

    as
    1. Kataria, K.K. & Vellaisamy, P., 2017. "Saigo space–time fractional Poisson process via Adomian decomposition method," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 69-80.
    2. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
    3. R. Pillai, 1990. "On Mittag-Leffler functions and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 157-161, March.
    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. Kataria, K.K. & Khandakar, M., 2022. "Extended eigenvalue–eigenvector method," Statistics & Probability Letters, Elsevier, vol. 183(C).
    2. K. K. Kataria & M. Khandakar, 2022. "Generalized Fractional Counting Process," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2784-2805, December.
    3. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    4. Zhang, Zhehao, 2018. "Renewal sums under mixtures of exponentials," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 281-301.
    5. Emad-Eldin Aly & Nadjib Bouzar, 2000. "On Geometric Infinite Divisibility and Stability," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 790-799, December.
    6. Levy, Edmond, 2021. "On the density for sums of independent Mittag-Leffler variates with common order," Statistics & Probability Letters, Elsevier, vol. 179(C).
    7. Kozubowski, Tomasz J., 2005. "A note on self-decomposability of stable process subordinated to self-decomposable subordinator," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 89-91, August.
    8. Chen, Wen & Liang, Yingjie, 2017. "New methodologies in fractional and fractal derivatives modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 72-77.
    9. Sánchez, Ewin, 2019. "Burr type-XII as a superstatistical stationary distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 443-446.
    10. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2020. "Geometric Tweedie regression models for continuous and semicontinuous data with variation phenomenon," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 33-58, March.
    11. Kozubowski, Tomasz J., 1998. "Mixture representation of Linnik distribution revisited," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 157-160, June.
    12. Kozubowski, Tomasz J., 2005. "A note on self-decomposability of stable process subordinated to self-decomposable subordinator," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 343-345, July.
    13. Beghin, Luisa & Macci, Claudio, 2013. "Large deviations for fractional Poisson processes," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1193-1202.
    14. Maheshwari, Aditya, 2023. "Tempered space fractional negative binomial process," Statistics & Probability Letters, Elsevier, vol. 196(C).
    15. Cho, Soobin & Kim, Panki, 2021. "Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 229-279.
    16. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    17. Pillai, R. N. & Jayakumar, K., 1995. "Discrete Mittag-Leffler distributions," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 271-274, May.
    18. Tomasz Kozubowski, 2000. "Exponential Mixture Representation of Geometric Stable Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 231-238, June.
    19. Agahi, Hamzeh & Alipour, Mohsen, 2019. "Mittag-Leffler-Gaussian distribution: Theory and application to real data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 227-235.
    20. Agahi, Hamzeh & Alipour, Mohsen, 2020. "Tsallis–Mittag-Leffler distribution and its applications in gas prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

    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:jotpro:v:32:y:2019:i:3:d:10.1007_s10959-018-0835-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.