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First hitting time of Brownian motion on simple graph with skew semiaxes

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  • Dassios, Angelos
  • Zhang, Junyi

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

  • Dassios, Angelos & Zhang, Junyi, 2022. "First hitting time of Brownian motion on simple graph with skew semiaxes," LSE Research Online Documents on Economics 111021, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:111021
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    File URL: http://eprints.lse.ac.uk/111021/
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    References listed on IDEAS

    as
    1. Becher, Christopher & Millard, Stephen & SoramÃÂäki, Kimmo, 2008. "The network topology of CHAPS Sterling," Bank of England working papers 355, Bank of England.
    2. Christopher Becher & Marco Galbiati & Merxe Tudela, 2008. "The timing and funding of CHAPS sterling payments," Economic Policy Review, Federal Reserve Bank of New York, vol. 14(Sep), pages 113-133.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Brownian motion; simple graph; first hitting time; Inverse Laplace transform; Bromwich integral;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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