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!

Coupling Markov chains

  1. Apr 28, 2009 #1
    1. The problem statement, all variables and given/known data
    Now that LaTeX is working again, maybe I can make the problem a little clearer.

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

    2. Relevant equations
    Markov property; coupling of Markov chains.

    3. The attempt at a solution

    I'm thinking no, except in the case where X and Y are independent. Otherwise

    \mathbb{P}[X_{n+1}=x_{n+1} | \mathcal{F}_Z] \neq \mathbb{P}[X_{n+1}=x_{n+1} | \mathcal{F}_X] \, ,

    where [tex]\mathcal{F}[/tex] is a filtration wrt the variable indicated.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

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

Similar Discussions: Coupling Markov chains
  1. Markov Chains (Replies: 9)

  2. Markov chain (Replies: 0)

  3. Markov Chain (Replies: 1)

  4. Markov Chain (Replies: 1)