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

Angelos Dassios () and Junyi Zhang ()
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Angelos Dassios: London School of Economics
Junyi Zhang: London School of Economics

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 1805-1831

Abstract: 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.

Keywords: Brownian motion; Simple graph; First hitting time; Inverse Laplace transform; Bromwich integral; 60J60; 60G40; 60J70 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09884-4

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