$(Y_n)_{n\in\{1,2..\}}$ is a i.i.d sequence f random variables.
$Y_1= 1$ with probability p and $Y_1=-k$ with probability $1-p$, where $0\leq p\leq 1$.
The process $(X_n)_n$ is defined as $X_0=0$ and $X_{n+1}=\max(X_n+Y_{n+1},0)$.
I have to prove that the process $(X_n)_n$ is an irreducibile Markov chain and I have to compute the matrix of the transition matrix P.
I'm tring to prove that $P(X_n+1=y |X_n=x,X_{n-1}=x_{n-1},..,X_1=x_1)$ does not depend on n but I am not able to conclude.
Any help ? Any hint to calculate P?