First hitting time of Brownian motion on simple graph with skew semiaxes
Dassios, A.
& Zhang, J.
(2022).
First hitting time of Brownian motion on simple graph with skew semiaxes.
Methodology and Computing in Applied Probability,
24(3), 1805 - 1831.
https://doi.org/10.1007/s11009-021-09884-4
& Zhang, J.
(2022).
First hitting time of Brownian motion on simple graph with skew semiaxes.
Methodology and Computing in Applied Probability,
24(3), 1805 - 1831.
https://doi.org/10.1007/s11009-021-09884-4
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.
