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Proving that an ODE is a markov process !

  1. Mar 29, 2007 #1
    I am trying to solve a problem from Van kampens book, page 73. I am trying to self learn stochastic processes for research sake !!

    A ODE is given: dx/dt = f(x). write the solution with initial values x0 and t0 in the form x = phi(x0, t - t0). Show that x obeys the defintion of the markov process with:

    p1|1(x,t|x0,t0) = delta[x - phi(x0, t - t0)].

    By delta, I mean the delta function. p1|1 is the transition probability(for jumps of any size).

    The solution of the ODE results in an exponential. It is not important.I am trying to integrate the joint distribution using the defintion of the heirarchy of distribtion functions(a bunch of delta functions). This does not however lead to the proof. I am out of ideas. Please help !

  2. jcsd
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