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applied stochastic processess

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    Ornstein-Uhlenbeck process is described by di⁄usion equation

    ∂P(z,t))/∂t = k*(∂P(z,t))/∂z + (B/2)*(∂^2P(z,t))/(∂z^2) -> eqn(1)

    Assuming initial condition Z(0) = 0; seek its solution in the form
    P(z; t) = 1/√(2πg(t)) exp⁡^(-z^2/2g(t) )
    Substitute this form into eq.1 and derive ODE for g(t): What is the appropriate initial condition?
    Find its solution and write a Â…nal solution for eq.1.

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Updated: November 14, 2013
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