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

Author

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  • 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
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    References listed on IDEAS

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    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. 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.
    4. 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.
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