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Thread: Erhenfest process

  1. #1
    Newbie pupupanda's Avatar
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    Erhenfest process

    Erhenfest process-untitled.png

    please help for this question
    thank you so much
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  2. #2
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    Re: Erhenfest process

    Hey pupupanda.

    Have you solved for the standard pi terms using the normal Markov method?
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  3. #3
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    Re: Erhenfest process

    I have no idea where to start
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  4. #4
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    Re: Erhenfest process

    There is a technique to solve for stationary states.

    Do you know what a stationary state is in a Markov process/chain?
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  5. #5
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    Re: Erhenfest process

    Quote Originally Posted by chiro View Post
    There is a technique to solve for stationary states.

    Do you know what a stationary state is in a Markov process/chain?
    Yes. I know what a stationary state is. How is this relate to the question?
    Thanks


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  6. #6
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    Re: Erhenfest process

    These are stationary states if the terminology you are using is correct.
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  7. #7
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    Re: Erhenfest process

    Quote Originally Posted by chiro View Post
    These are stationary states if the terminology you are using is correct.
    I don't know how to prove it. Stationary distribution is a stochastic process {Xt: t>_0} is stationary if for any k>_ 0 and any m>_t, the joint distribution of (Xt,....Xm) is the same as the joint distribution of (Xt+k,...Xm+k), right?
    I don't know how to apply it to this problem



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  8. #8
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    Re: Erhenfest process

    Stationary states can be derived with an expression for the values of the matrix.

    The idea is that pi_(j) = Sum [i=0 to M] pi(i) * p(i,j) where pi(x) is the stationary probability for state x and p(i,j) is the probability value in the Markov chain matrix.

    They are also probabilities meaning they are between 0 and 1 inclusive and all add up to unity.
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  9. #9
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    Re: Erhenfest process

    Quote Originally Posted by chiro View Post
    Stationary states can be derived with an expression for the values of the matrix.

    The idea is that pi_(j) = Sum [i=0 to M] pi(i) * p(i,j) where pi(x) is the stationary probability for state x and p(i,j) is the probability value in the Markov chain matrix.

    They are also probabilities meaning they are between 0 and 1 inclusive and all add up to unity.
    I don't know how to work out the transition matrix for this case



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    Re: Erhenfest process

    can you help me to guidance where should I start this? then I can to continue.
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  11. #11
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    Re: Erhenfest process

    Can you state information about the process? Anything on your notes regarding transition probabilities for this process?
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  12. #12
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    Re: Erhenfest process

    Quote Originally Posted by chiro View Post
    Can you state information about the process? Anything on your notes regarding transition probabilities for this process?
    I already solve the problem with the stationary distribution. Thanks


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