The first returning speed and the last exit speed of a type of Markov chain

Huizeng Zhang, Minzhi zhao, Lei wang

Let $\{X_n\}$ be a Markov chain with transition probability $p_{ij}=a_{j-(i-1{)}^{+}},\forall i,j\ge 0$, where $a_j=0$ provided $j<0$, $a_0>0$, $a_0+a_1<1$ and $\sum_{n=0}^\infty a_n=1…