IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v24y2022i3d10.1007_s11009-021-09884-4.html
   My bibliography  Save this article

First Hitting Time of Brownian Motion on Simple Graph with Skew Semiaxes

Author

Listed:
  • Angelos Dassios

    (London School of Economics)

  • Junyi Zhang

    (London School of Economics)

Abstract

Consider a stochastic process that lives on n-semiaxes emanating from a common origin. On each semiaxis it behaves as a Brownian motion and at the origin it chooses a semiaxis randomly. In this paper we study the first hitting time of the process. We derive the Laplace transform of the first hitting time, and provide the explicit expressions for its density and distribution functions. Numerical examples are presented to illustrate the application of our results.

Suggested Citation

  • Angelos Dassios & Junyi Zhang, 2022. "First Hitting Time of Brownian Motion on Simple Graph with Skew Semiaxes," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1805-1831, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09884-4
    DOI: 10.1007/s11009-021-09884-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-021-09884-4
    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/s11009-021-09884-4?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. Soramäki, Kimmo & Bech, Morten L. & Arnold, Jeffrey & Glass, Robert J. & Beyeler, Walter E., 2007. "The topology of interbank payment flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 317-333.
    2. Karatzas, Ioannis & Yan, Minghan, 2019. "Semimartingales on rays, Walsh diffusions, and related problems of control and stopping," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 1921-1963.
    3. Angelos Dassios & Shanle Wu, 2010. "Perturbed Brownian motion and its application to Parisian option pricing," Finance and Stochastics, Springer, vol. 14(3), pages 473-494, September.
    4. Vassilis G. Papanicolaou & Effie G. Papageorgiou & Dimitris C. Lepipas, 2012. "Random Motion on Simple Graphs," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 285-297, June.
    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. Lempa, Jukka & Mordecki, Ernesto & Salminen, Paavo, 2024. "Diffusion spiders: Green kernel, excessive functions and optimal stopping," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

    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. Angelos Dassios & Junyi Zhang, 2020. "Parisian Time of Reflected Brownian Motion with Drift on Rays and Its Application in Banking," Risks, MDPI, vol. 8(4), pages 1-14, December.
    2. Lempa, Jukka & Mordecki, Ernesto & Salminen, Paavo, 2024. "Diffusion spiders: Green kernel, excessive functions and optimal stopping," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    3. Galbiati, Marco & Soramäki, Kimmo, 2011. "An agent-based model of payment systems," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 859-875, June.
    4. Claus Puhr & Reinhardt Seliger & Michael Sigmund, 2012. "Contagiousness and Vulnerability in the Austrian Interbank Market," Financial Stability Report, Oesterreichische Nationalbank (Austrian Central Bank), issue 24, pages 62-78.
    5. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, August.
    6. Fariba Karimi & Matthias Raddant, 2016. "Cascades in Real Interbank Markets," Computational Economics, Springer;Society for Computational Economics, vol. 47(1), pages 49-66, January.
    7. Cetina, Jill & Paddrik, Mark & Rajan, Sriram, 2018. "Stressed to the core: Counterparty concentrations and systemic losses in CDS markets," Journal of Financial Stability, Elsevier, vol. 35(C), pages 38-52.
    8. Gautier M Krings & Jean-François Carpantier & Jean-Charles Delvenne, 2014. "Trade Integration and Trade Imbalances in the European Union: A Network Perspective," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-14, January.
    9. Kuzubaş, Tolga Umut & Saltoğlu, Burak & Sever, Can, 2016. "Systemic risk and heterogeneous leverage in banking networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 358-375.
    10. Bech, Morten L. & Atalay, Enghin, 2010. "The topology of the federal funds market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5223-5246.
    11. Dassios, Angelos & Li, Luting, 2020. "Explicit asymptotic on first passage times of diffusion processes," LSE Research Online Documents on Economics 103087, London School of Economics and Political Science, LSE Library.
    12. Yoshiharu Maeno & Kenji Nishiguchi & Satoshi Morinaga & Hirokazu Matsushima, 2014. "Impact of credit default swaps on financial contagion," Papers 1411.1356, arXiv.org.
    13. Demidov, Denis & Frahm, Klaus M. & Shepelyansky, Dima L., 2020. "What is the central bank of Wikipedia?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    14. Klaus Abbink & Ronald Bosman & Ronald Heijmans & Frans van Winden, 2017. "Disruptions in Large-Value Payment Systems: An Experimental Approach," International Journal of Central Banking, International Journal of Central Banking, vol. 13(4), pages 63-95, December.
    15. Ricardo Mariño-Martínez & Carlos León & Carlos Cadena-Silva, 2020. "Las entidades de contrapartida central en la mitigación del riesgo de contraparte y de liquidez: El caso de los derivados cambiarios en Colombia," Borradores de Economia 1101, Banco de la Republica de Colombia.
    16. Martínez, Constanza & León, Carlos, 2016. "The cost of collateralized borrowing in the Colombian money market: Does connectedness matter?," Journal of Financial Stability, Elsevier, vol. 25(C), pages 193-205.
    17. Liberati, Caterina & Marzo, Massimiliano & Zagaglia, Paolo & Zappa, Paola, 2012. "Structural distortions in the Euro interbank market: the role of 'key players' during the recent market turmoil," MPRA Paper 40223, University Library of Munich, Germany.
    18. Ms. Sheri M. Markose, 2012. "Systemic Risk from Global Financial Derivatives: A Network Analysis of Contagion and Its Mitigation with Super-Spreader Tax," IMF Working Papers 2012/282, International Monetary Fund.
    19. Lester, Benjamin & Weill, Pierre-Olivier & Hugonnier, Julien, 2022. "Heterogeneity in decentralized asset markets," Theoretical Economics, Econometric Society, vol. 17(3), July.
    20. Elosegui, Pedro & Forte, Federico D. & Montes-Rojas, Gabriel, 2022. "Network structure and fragmentation of the Argentinean interbank markets," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 3(3).

    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:24:y:2022:i:3:d:10.1007_s11009-021-09884-4. 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.