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

Angelos Dassios; Junyi Zhang

doi:10.1007/s11009-021-09884-4

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

Angelos Dassios, Junyi Zhang

Research output: Journal article publication › Journal article › Academic research › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	1805-1831
Number of pages	27
Journal	Methodology and Computing in Applied Probability
Volume	24
Issue number	3
DOIs	https://doi.org/10.1007/s11009-021-09884-4
Publication status	Published - Sept 2022
Externally published	Yes

Keywords

Bromwich integral
Brownian motion
First hitting time
Inverse Laplace transform
Simple graph

ASJC Scopus subject areas

Statistics and Probability
General Mathematics

More information

10.1007/s11009-021-09884-4

Cite this

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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 = "Bromwich integral, Brownian motion, First hitting time, Inverse Laplace transform, Simple graph",

author = "Angelos Dassios and Junyi Zhang",

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N2 - 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.

AB - 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.

KW - Bromwich integral

KW - Brownian motion

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KW - Inverse Laplace transform

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JO - Methodology and Computing in Applied Probability

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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