Discrete time Markov chain

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

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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