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Markov chains

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data
    Let Y1,Y2,.... be independent identically distributed random variables with
    P(Y1=1) = P(Y1=-1) = 1/2 and set X0 = 1, Xn=X0 + Y1 +...+ Yn for n >= 1. Define
    H0 = inf { n >= 0 : Xn = 0}.
    Find the probability generating function Φ(s) = E(sH0).


    2. Relevant equations



    3. The attempt at a solution
    Actually, this is grad. level course, but
    I do not have much some background about probability.
    I don't know whether I can get the values of X2, X3,... Xn by using Y1 =1 = Y1 = -1...
    Is it possible?
     
  2. jcsd
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