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Markov chains

  1. Apr 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Let [tex]X[/tex] and Y be Markov chains on the set Z of integers. Is the sequence Z_n = X_n + Y_n necessarily a Markov chain?

    2. Relevant equations
    Markov property:

    P[X_n=x_n | X_{n-1}=x_{n-1},...,X_0=X_0] = P[X_n=x_n|X_{n-1}=x_{n-1}]

    3. The attempt at a solution

    I'm thinking it is, because P[X+Y|Z] = P[X|Z]+P[Y|Z], and both X and Y have the Markov property; moreover, P[X|Z] = P[X|X_{n-1}, ..., X_0] because X doesn't care about Y in the first place. Does this seem right?
    Last edited: Apr 22, 2009
  2. jcsd
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