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Dassios A, Zhang J. First Hitting Time of Brownian Motion on Simple Graph with Skew Semiaxes. Methodol Comput Appl Probab 2022. [DOI: 10.1007/s11009-021-09884-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
AbstractConsider 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.
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The first passage time on the (reflected) Brownian motion with broken drift hitting a random boundary. Stat Probab Lett 2021. [DOI: 10.1016/j.spl.2021.109040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Dong Q, Cui L. First Hitting Time Distributions for Brownian Motion and Regions with Piecewise Linear Boundaries. Methodol Comput Appl Probab 2018. [DOI: 10.1007/s11009-018-9638-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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