IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v192y2026ics030441492500239x.html

Sticky diffusions on star graphs: Characterization and Itô formula

Author

Listed:
  • Berry, Jules
  • Colantoni, Fausto

Abstract

In this paper, we investigate continuous diffusions on star graphs with sticky behaviour at the vertex. These are Markov processes with continuous paths having a positive occupation time at the vertex. We characterize the sticky diffusions as time changed nonsticky diffusions by adapting the classical technique of Itô and McKean. We prove a form of Itô formula, also known as Freidlin–Sheu formula, for this type of process. As an intermediate step, we also obtain a stochastic differential equation satisfied by the radial component of the process. These results generalize those already known for sticky diffusions on a half-line and skew sticky diffusions on the real line.

Suggested Citation

  • Berry, Jules & Colantoni, Fausto, 2026. "Sticky diffusions on star graphs: Characterization and Itô formula," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:spapps:v:192:y:2026:i:c:s030441492500239x
    DOI: 10.1016/j.spa.2025.104795
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441492500239X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104795?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. Touhami, Wajdi, 2021. "On skew sticky Brownian motion," Statistics & Probability Letters, Elsevier, vol. 173(C).
    2. Albeverio, Sergio & Mastrogiacomo, Elisa, 2022. "Large deviation principle for spatial economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    3. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    4. Murray H. Protter & Hans F. Weinberger, 1984. "Maximum Principles in Differential Equations," Springer Books, Springer, number 978-1-4612-5282-5, August.
    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. Noha Almulla & Rita Ferreira & Diogo Gomes, 2017. "Two Numerical Approaches to Stationary Mean-Field Games," Dynamic Games and Applications, Springer, vol. 7(4), pages 657-682, December.
    2. V. N. Kolokoltsov & O. A. Malafeyev, 2018. "Corruption and botnet defense: a mean field game approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 977-999, September.
    3. Ruxin Chen & Zeqiang Zhang, 2025. "From Individual Learning to Market Equilibrium: Correcting Structural and Parametric Biases in RL Simulations of Economic Models," Papers 2507.18229, arXiv.org, revised Oct 2025.
    4. Naci Saldi & Tamer Başar & Maxim Raginsky, 2019. "Approximate Nash Equilibria in Partially Observed Stochastic Games with Mean-Field Interactions," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1006-1033, August.
    5. Alberto Bressan & Khai T. Nguyen, 2023. "Generic Properties of First-Order Mean Field Games," Dynamic Games and Applications, Springer, vol. 13(3), pages 750-782, September.
    6. Hoang, Lê Nguyên & Soumis, François & Zaccour, Georges, 2019. "The return function: A new computable perspective on Bayesian–Nash equilibria," European Journal of Operational Research, Elsevier, vol. 279(2), pages 471-485.
    7. Diogo A. Gomes & João Saúde, 2021. "A Mean-Field Game Approach to Price Formation," Dynamic Games and Applications, Springer, vol. 11(1), pages 29-53, March.
    8. Adriano Festa & Simone Göttlich & Michele Ricciardi, 2025. "Forward-Forward Mean Field Games in Mathematical Modeling with Application to Opinion Formation and Voting Models," Dynamic Games and Applications, Springer, vol. 15(2), pages 664-692, May.
    9. Giorgio Fabbri & Silvia Faggian & Salvatore Federico & Fausto Gozzi, 2025. "Optimal Control in Infinite Dimensional Spaces and Economic Modeling: State of the Art and Perspectives," Working Papers 2025-06, Grenoble Applied Economics Laboratory (GAEL).
    10. Luo, Peng & Tangpi, Ludovic, 2024. "Laplace principle for large population games with control interaction," Stochastic Processes and their Applications, Elsevier, vol. 171(C).
    11. V. N. Kolokoltsov & O. A. Malafeyev, 2017. "Mean-Field-Game Model of Corruption," Dynamic Games and Applications, Springer, vol. 7(1), pages 34-47, March.
    12. Naci Saldi & Tamer Bas¸ ar & Maxim Raginsky, 2020. "Approximate Markov-Nash Equilibria for Discrete-Time Risk-Sensitive Mean-Field Games," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1596-1620, November.
    13. Naci Saldi & Tamer Başar & Maxim Raginsky, 2023. "Partially Observed Discrete-Time Risk-Sensitive Mean Field Games," Dynamic Games and Applications, Springer, vol. 13(3), pages 929-960, September.
    14. Berkay Anahtarci & Can Deha Kariksiz & Naci Saldi, 2023. "Q-Learning in Regularized Mean-field Games," Dynamic Games and Applications, Springer, vol. 13(1), pages 89-117, March.
    15. Fabio Bagagiolo & Dario Bauso & Raffaele Pesenti, 2016. "Mean-Field Game Modeling the Bandwagon Effect with Activation Costs," Dynamic Games and Applications, Springer, vol. 6(4), pages 456-476, December.
    16. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2021. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Dynamic Games and Applications, Springer, vol. 11(3), pages 463-490, September.
    17. Piotr Więcek, 2024. "Multiple-Population Discrete-Time Mean Field Games with Discounted and Total Payoffs: The Existence of Equilibria," Dynamic Games and Applications, Springer, vol. 14(4), pages 997-1026, September.
    18. Dario Bauso & Hamidou Tembine & Tamer Başar, 2016. "Robust Mean Field Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 277-303, September.
    19. Qing Tang & Fabio Camilli, 2020. "Variational Time-Fractional Mean Field Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 573-588, June.
    20. Zhu, Zheng & Ke, Jintao & Wang, Hai, 2021. "A mean-field Markov decision process model for spatial-temporal subsidies in ride-sourcing markets," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 540-565.

    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:eee:spapps:v:192:y:2026:i:c:s030441492500239x. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.