\begin{cases} \mathbb{P}\left\{X_{n+1}=X_{n}+b \sqrt{p} \mid X_{n}=x\right\}=e^{-\sqrt{p} X_{n}} \\ \mathbb{P}\left\{X_{n+1}=a X_{n} \mid X_{n}=x\right\}=(1-c)\left(1-e^{-\sqrt{p} X_{n}}\right) \\ \mathbb{P}\left\{X_{n+1}=0 \mid X_{n}=x\right\}=c\left(1-e^{-\sqrt{p} X_{n}}\right) \end{cases}
Could anyone tell me how to show that the above process has a unique invariant measure for all $a\in (0,1), b\in (0,\infty), c\in [0,1]$?