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Student Support Forum: 'Stochastic ODE' topicStudent Support Forum > General > Archives > "Stochastic ODE"

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John Barber
10/29/01 10:45am

Thanks!

Actually, I think the random function CAN be defined numerically in advance. Since
Random[NormalDistribution[0,Sqrt[1/(1+q[t]^2)]]]
is statistically the same as
Random[NormalDistribution[0,1]]/Sqrt[1+q[t]^2],
I can write my set of ODE's as:

q'[t]==p[t]
p'[t]==-(1+ (Q[t]^2)/(1+q[t]^2))q[t]

where Q[t]=Random[NormalDistribution[0,1]] at each instant in time.
I generated Q[t] in advance by creating a table of such random numbers at many time values, and then invoking Interpolation[...]. The solutions generated look just like those in the attachement of the above reply, but NDSolve only needs to be called once. See this attached notebook.

Attachment: StochasticODE.nb, 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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