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Thread: Martingale

  1. #16
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    Re: Martingale




    Please forgive me I am unsure what you mean use the conditional expectation of X_{n+1}.

    do you mean that after using the linearity property on the second line that

    aE[X_{n+1}|X_n,...,X_1] + E[X_n|X_n,...,X_1] \neq\ aX_n + X_{n-1}

  2. #17
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    Re: Martingale

    So look at the question statement again. What property is given?

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  4. #18
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    Re: Martingale

    Do you mean that r.v. {X_n} has finite expectation and satisfy

    E[X_{n+1} | X_n,..,X_0]= \alpha X_n +\beta X_{n-1}
    Last edited by LED2127; 04-03-2012 at 09:12 AM.

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    Re: Martingale

    That would definitely be something to keep in mind.
    I don't have emotions and sometimes that makes me very sad.

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  7. #20
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    Re: Martingale


    Let me try this again,
    considering:
    aE[X_{n+1}|X_n,..,X_1]+E[X_n|X_n,...,X_1] =Y_n

    and if I use the given property

    = a[\alpha X_n+\beta X_{n-1}] +X_{n-1} = Y_n

    and Y_n = aX_n+X_{n-1}

    = a[\alpha X_n+\beta X_{n-1}] +X_{n-1} = aX_n+X_{n-1}
    Last edited by LED2127; 04-03-2012 at 09:11 AM.

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