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$ (X_n : n = 0, 1, 2, ...) $ is a Markov chain with state space $(1,2,...,10)$. Then which of the following is the correct answer?

  1. ($X_n+X_{n-1} : n = 1, 2, ...$) is a Markov chain.
  2. ($X_n-X_{n-1} : n = 1, 2, ...$) is a Markov chain.
  3. ($X_nX_{n-1} : n = 1, 2, ...$) is a Markov chain.
  4. ($\frac {X_n}{X_{n-1}} : n = 1, 2, ...$) is a Markov chain.
  5. None of the above is correct.

Is it option 5 is the correct answer because we cannot do the inverse of the function? Just like option 1, we asuume $X_n=4$ and $X_{n-1}=6$, then $X_n+X_{n-1}=10$, but we cannot do the inverse.

user109403
  • 289
  • See this question: http://math.stackexchange.com/questions/27507/transformation-of-state-space-that-preserves-markov-property – Math1000 Feb 22 '16 at 09:30
  • is it mean that my explanation of this problem is correct since the function are not one-to-one?? – user109403 Feb 22 '16 at 09:38

0 Answers0