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Math Help - HARD - derivation of general solution to K Backward Equation

  1. #1
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    HARD - derivation of general solution to K Backward Equation

    hi all

    so this question is quite tough to answer.

    the fundamental solution of the kolmogorov backward equation is:

    dp/dt = Lp = 1/2 D^2(x) d2p/dx2 + M(x)dp/dx

    where D is the variance and M is the mean.

    given a stationary distribution Lp = 0 so if we have a function T(x)

    1/2 D^2(x) T''(x) + M(x)T'(x) = 0

    a solution to this is the harmonic function

    now i want to know how is

    T'(x) = C exp(-int_xo^x 2M(s)/D^2(s) ds )

    and

    T(X) = int^x exp(-int_xo^x 2M(y)/D^2(y) dy ) du


    My kingdom for latex..... i hope someone can help...
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  2. #2
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    Nov 2006
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    perhaps i have to do this

    1/2 D^2(x) T''(x) + M(x)T'(x) = 0

    h = T'(x)

    h'/h = 2M(x) / D^2(x)


    maybe? whats the solution of this?

    cheers all
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