Quasi-stationary distributions for time-changed symmetric $α$-stable processes killed upon hitting zero

Zhe-Kang Fang, Yong-Hua Mao, Tao Wang

Published 2023-06-13Version 1

For a time-changed symmetric $\alpha$-stable process killed upon hitting zero, under the condition of entrance from infinity, we prove the existence and uniqueness of quasi-stationary distribution (QSD). The exponential convergence to the QSD from any initial distribution is proved under conditions on transition densities.