1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted