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| Ergodicity and First Passage Probability of Regime-Switching Geometric Brownian Motions |
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Citation： |
Jinghai SHAO.Ergodicity and First Passage Probability of Regime-Switching Geometric Brownian Motions[J].Chinese Annals of Mathematics B,2018,39(4):739~754 |
| Page view： 767
Net amount： 778 |
Authors： |
Jinghai SHAO; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11301030, 11431014). |
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| Abstract： |
A regime-switching geometric Brownian motion is used to model a
geometric Brownian motion with its coefficients changing randomly
according to a Markov chain. In this work, the author gives a
complete characterization of the recurrent property of this process.
The long time behavior of this process such as its $p$-th moment is
also studied. Moreover, the quantitative properties of the
regime-switching geometric Brownian motion with two-state switching
are investigated to show the difference between geometric Brownian
motion with switching and without switching. At last, some estimates
of its first passage probability are established. |
Keywords： |
Ergodicity, Regime-switching diffusions, Lyapunov functions, Firstpassage probability |
Classification： |
60A10, 60J60, 60J10 |
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