Strongly quasi-mixing properties for one-dimensional diffusion processes with killing *

In this paper, we establish sufficient conditions for the existence of strongly (uniformly and exponentially) quasi-mixing limits of one-dimensional diffusion processes with killing. As a by-product, these conditions also ensure that the considered processes have strong quasi-ergodicity, strong fractional quasi-ergodicity and uniform mean-ratio quasi-ergodicity. Moreover, the quasi-ergodic speeds of these three quasi-ergodicities are also characterized.