Existence and uniqueness of mean-ratio quasi-stationary distribution for one-dimensional diffusions

Hanjun Zhang, Guoman He

Published 2014-09-29Version 1

In this paper, we study mean-ratio quasi-stationary distribution (MRQSD) for one-dimensional diffusion $X$ killed at 0, when $+\infty$ is an entrance boundary and 0 is an exit boundary. More precisely, we not only show that the process is $R$-positive, but also prove the existence and uniqueness of MRQSD by using the spectral theory tool. As a consequence, this unique MRQSD is just the stationary distribution of $Q$-process.