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Math Help - Problem in martingale.

  1. #1
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    Problem in martingale.

    (Xn, Bn)n>=0 is a martingale. Xn+1/Xn belong to L'. Prove that E(Xn+1/Xn) = 1.

    I know that I have to use Conditional expectation theory here, but i dont know how to proceed, though it looks to be a simple problem. If anyone know how to prove, please post the solution

    Thanks
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  2. #2
    Moo
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    Hello,

    What is Bn ?
    And please please please, use the LaTeX... Not sure : is Xn+1/Xn the random variable Xn+1 conditioned on Xn ?
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  3. #3
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    Bn is the filtration of the σ-algebra B of the space (Ω,B,P), and yes Xn+1 is conditioned on Xn.
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  4. #4
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    Then I don't understand... Because E[X_{n+1}\mid X_n] is not always equal to 1...
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  5. #5
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    that's just the question. please note that my question says that it belongs to the integrable space L'

    I think the property that Xn is a sub σ-algebra of the filtration Bn must be used,then the answer is immediate. But I amnot sure.

    Any i/p is appreciated.


    Thanks in advance.
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