# Discrete time Markov chain

#### eXorikos

1. The problem statement, all variables and given/known data
Let $$\left( X_n \right)_{n \geq 0}$$ be a Markov chain on {0,1,...} with transition probabilities given by:
$$p_{01} = 1$$, $$p_{i,i+1} + p_{i,i-1} = 1$$, $$p_{i,i+1} = \left(\frac{i+1}{i} \right)^2 p_{i,i-1}$$
Show that if $$X_0 = 0$$ then the probability that $$X_n \geq 1$$ for all $$n \geq 1$$ is 6/$$\pi^2$$

3. The attempt at a solution
I really don't have an attempt. I think I have to use the master equation for discrete time since it's a stationary distribution for n>0. I've been thinking about it more than it seems by these two sentences but I'm quite stuck...

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