Ergodicity and First Passage Probability of Regime-Switching Geometric Brownian Motions

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 / First passage probability

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