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...
 

Want to reply to this thread?

"Discrete time Markov chain" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Top Threads

Top