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Re: Re: White Noise in Simulation

• To: mathgroup at smc.vnet.net
• Subject: [mg103607] Re: [mg103576] Re: White Noise in Simulation
• From: Dan Dubin <ddubin at ucsd.edu>
• Date: Wed, 30 Sep 2009 04:59:36 -0400 (EDT)
• References: <h9p69i$vu$1@smc.vnet.net> <200909291136.HAA25463@smc.vnet.net>

>On Sep 27, 10:16 pm, SlipperyWeasel <slipperywea... at gmail.com> wrote:
>>  I am trying to add random noise to a function inside an NDSolve
>>  function.  Is there a good way to add a "noise function" in my model?
>
>for example, my system is:  x'[t] == x[t] + Sin[t] + v
>where v is Gaussian white noise.
>
>v has to be a continuous function of t in order to use NDSolve on the
>ODE, but it also should be uncorrelated.  How can I make this a
>continuous function while still making it uncorrelated?


Your noise function must have a finite correlation time to be 
realizable, and be a continuous function to work with NDSolve. Here 
is a continuous random function a(t, dt) consisting of a series of 
peaks of width dt with random amplitudes amp[n] between +-1


amp[n_] := amp[n] = RandomReal[{-1, 1}];
a[t_, dt_] := amp[Floor[t/dt]] Sin[2 Pi Mod[t, dt]/dt]^2

-- 
Dan Dubin

• References:
  • Re: White Noise in Simulation
    • From: SlipperyWeasel <slipperyweasel@gmail.com>