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 Author Comment/Response John Barber 09/13/01 3:47pm Hi Folks: I have a small system of stochastic ODE's to solve. Here is the system: q'[t]==p[t] p'[t]==-(1+Q[t]^2)q[t] here Q[t] is a random variable, i.e., it takes on a different random value at every instant of time. What makes this difficult is that the statistics of Q depend on the value of q[t] at that moment. Specifically, at each instant in time, Q is sampled from a normal distribution with mean zero and variance 1/(1+q[t]^2). I wish to be able to numerically solve this ODE, and thus generate random trajectories in the (q,p) plane. (Naturally, each one will be different.) I can't seem to get it to work. I've tried the following, to no avail. (Yes, I remembered to load the Statistics`ContinuousDistributions` package): NDSolve[{q'[t] == p[t], p'[t] == -(1 + (Random[NormalDistribution[0, Sqrt[1/(1 + q[t]^2)]]])^2)q[ t], q[0] == 1, p[0] == 0}, {q, p}, {t, 0, 20}] This generates the warning that the second argument of NormalDistribution[] is not a machine sized number. Then, I tried creating a function and doing the following: Q[b_] := Random[NormalDistribution[0, Sqrt[1/(1 + b^2)]]]; NDSolve[{q'[t] == p[t], p'[t] == -(1 + Q[q[t]]^2)q[t], q[0] == 1, p[0] == 0}, {q, p}, {t, 0, 20}] This generated the same error message. Is it possible to do what I am trying to do in Mathematica, or do I have to write my own code? (Just for reference: a correct solution to the above ODE should trace out a wiggly, Brownian-looking trajectory in the (q,p) plane that goes around in a very rough circle in the clockwise direction.) Thanks, John Barber URL: ,

 Subject (listing for 'Stochastic ODE') Author Date Posted Stochastic ODE John Barber 09/13/01 3:47pm Re: Stochastic ODE Forum Modera... 10/05/01 3:26pm Re: Stochastic ODE John Barber 10/05/01 7:15pm Re: Stochastic ODE Henry Lamb 10/15/01 03:45am Re: Stochastic ODE John Barber 10/25/01 11:30am Re: Stochastic ODE Henry Lamb 10/28/01 01:17am Re: Stochastic ODE John Barber 10/29/01 10:45am
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