IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v186y2024ics0960077924008592.html
   My bibliography  Save this article

Analytic expression of the probability density function for the first-passage time in birth-death processes

Author

Listed:
  • Park, Seong Jun
  • Choi, M.Y.

Abstract

Birth-death processes occur throughout the universe, and the rates of birth and death generally depend on the system size (the number of products or customers), varying with each event. Moreover, deriving an analytic expression for the probability density function for birth-death processes remains challenging despite the interest in the first-passage time (when the system size first reaches a specific threshold). This work derives the probability density function of the first-passage time without approximations based on considering all cases where the number of products reaches a threshold at each birth instance, providing an analytic expression for the statistics of the first-passage time. This work offers a promising new approach to investigating the first-passage time in birth-death processes.

Suggested Citation

  • Park, Seong Jun & Choi, M.Y., 2024. "Analytic expression of the probability density function for the first-passage time in birth-death processes," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
  • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008592
    DOI: 10.1016/j.chaos.2024.115307
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924008592
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2024.115307?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. Palacios, JoséLuis & Tetali, Prasad, 1996. "A note on expected hitting times for birth and death chains," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 119-125, October.
    2. Seong Jun Park & Sanggeun Song & Gil-Suk Yang & Philip M. Kim & Sangwoon Yoon & Ji-Hyun Kim & Jaeyoung Sung, 2018. "The Chemical Fluctuation Theorem governing gene expression," Nature Communications, Nature, vol. 9(1), pages 1-12, December.
    3. Joel E Cohen, 2004. "Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better," PLOS Biology, Public Library of Science, vol. 2(12), pages 1-1, December.
    4. Aleksejus Kononovicius & Vygintas Gontis, 2019. "Approximation of the first passage time distribution for the birth-death processes," Papers 1902.00924, arXiv.org.
    5. Attila Becskei & Luis Serrano, 2000. "Engineering stability in gene networks by autoregulation," Nature, Nature, vol. 405(6786), pages 590-593, June.
    6. Masuda, Yasushi, 1988. "First passage times of birth-death processes and simple random walks," Stochastic Processes and their Applications, Elsevier, vol. 29(1), pages 51-63.
    7. Giorno, Virginia & Nobile, Amelia G., 2020. "On a class of birth-death processes with time-varying intensity functions," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    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. Giorno, Virginia & Nobile, Amelia G., 2022. "On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. Bapat, R.B., 2011. "On the first passage time of a simple random walk on a tree," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1552-1558, October.
    3. Avraham E Mayo & Yaakov Setty & Seagull Shavit & Alon Zaslaver & Uri Alon, 2006. "Plasticity of the cis-Regulatory Input Function of a Gene," PLOS Biology, Public Library of Science, vol. 4(4), pages 1-1, March.
    4. Cencetti, Giulia & Battiston, Federico & Carletti, Timoteo & Fanelli, Duccio, 2020. "Generalized patterns from local and non local reactions," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Palacios, José Luis, 2000. "A note on circular Markov chains," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 301-306, April.
    6. Chen Jia & Ramon Grima, 2024. "Holimap: an accurate and efficient method for solving stochastic gene network dynamics," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    7. Kyung H Kim & Herbert M Sauro, 2012. "Adjusting Phenotypes by Noise Control," PLOS Computational Biology, Public Library of Science, vol. 8(1), pages 1-14, January.
    8. Elisa Setten & Alessandra Castagna & Josué Manik Nava-Sedeño & Jonathan Weber & Roberta Carriero & Andreas Reppas & Valery Volk & Jessica Schmitz & Wilfried Gwinner & Haralampos Hatzikirou & Friedrich, 2022. "Understanding fibrosis pathogenesis via modeling macrophage-fibroblast interplay in immune-metabolic context," Nature Communications, Nature, vol. 13(1), pages 1-22, December.
    9. Alexander Anders & Bhaswar Ghosh & Timo Glatter & Victor Sourjik, 2020. "Design of a MAPK signalling cascade balances energetic cost versus accuracy of information transmission," Nature Communications, Nature, vol. 11(1), pages 1-10, December.
    10. Najme Khorasani & Mehdi Sadeghi & Abbas Nowzari-Dalini, 2020. "A computational model of stem cell molecular mechanism to maintain tissue homeostasis," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-25, July.
    11. Simeon D. Castle & Michiel Stock & Thomas E. Gorochowski, 2024. "Engineering is evolution: a perspective on design processes to engineer biology," Nature Communications, Nature, vol. 15(1), pages 1-10, December.
    12. Giorno, Virginia & Nobile, Amelia G., 2023. "On a time-inhomogeneous diffusion process with discontinuous drift," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    13. Tobias May & Lee Eccleston & Sabrina Herrmann & Hansjörg Hauser & Jorge Goncalves & Dagmar Wirth, 2008. "Bimodal and Hysteretic Expression in Mammalian Cells from a Synthetic Gene Circuit," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-7, June.
    14. Gentian Buzi & Mustafa Khammash, 2016. "Implementation Considerations, Not Topological Differences, Are the Main Determinants of Noise Suppression Properties in Feedback and Incoherent Feedforward Circuits," PLOS Computational Biology, Public Library of Science, vol. 12(6), pages 1-16, June.
    15. James R. Carey, 2008. "Biodemography: Research prospects and directions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 19(50), pages 1749-1758.
    16. José Luis Palacios & Daniel Quiroz, 2016. "Birth and Death Chains on Finite Trees: Computing their Stationary Distribution and Hitting Times," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 487-498, June.
    17. Cazelles, Bernard & Chavez, Mario & Courbage, Maurice, 2012. "Editorial," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 1-1.
    18. Haiyan, Chen & Fuji, Zhang, 2004. "The expected hitting times for graphs with cutpoints," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 9-17, January.
    19. Alex J. H. Fedorec & Neythen J. Treloar & Ke Yan Wen & Linda Dekker & Qing Hsuan Ong & Gabija Jurkeviciute & Enbo Lyu & Jack W. Rutter & Kathleen J. Y. Zhang & Luca Rosa & Alexey Zaikin & Chris P. Bar, 2024. "Emergent digital bio-computation through spatial diffusion and engineered bacteria," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    20. Luca Cardelli & Rosa D Hernansaiz-Ballesteros & Neil Dalchau & Attila Csikász-Nagy, 2017. "Efficient Switches in Biology and Computer Science," PLOS Computational Biology, Public Library of Science, vol. 13(1), pages 1-16, January.

    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:eee:chsofr:v:186:y:2024:i:c:s0960077924008592. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.