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Math Help - Markov Processes

  1. #1
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    Markov Processes! (Markov Chain)

    Hi there...

    Let {X} be a Markov chain and {T} be a finite stopping time. Show that {(X_{n+T})}_{n \geq 0} defines a Markov chain, taking care of stating the relevant filtration.

    Any help would be greatly appreciated..
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  2. #2
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    \mathbb{P}(X_{n+T}|\sigma(X_{s+T}:s\leq m))=\sum \mathbb{P}(X_{n+i}|\sigma(X_{s+i}:s\leq m))\mathbb{P}(T=i)
    =\sum \mathbb{P}(X_{n+i}|\sigma(X_{m+i}))\mathbb{P}(T=i)  =\mathbb{P}(X_{n+T}|\sigma(X_{m+T}))

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