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First step analysis hitting time

  1. Apr 10, 2013 #1
    I'm having a little trouble understanding the mean hitting time of a random walk, with p(i,j) = p if j=i+1, q if j=i-1 and 0 otherwise. 0 is an absorbing state and no upper absorbing state ie. dealer has unlimited amount of money.

    Need to work out the mean hitting times k(i)(0) for i=0,1,2 etc.

    I believe that i is the initial starting point however wouldn't the mean hitting time be different for each i? The way the question is worded sounds like same answer for all i.

    Need to calculate for the cases where p<q, p=q and p>q and I have the theorem k(i)(0) = sum (over j does not equal 0) of p(i,j)k(j,0)
    I don't get what this theorem means?

  2. jcsd
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