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The equation has the following form:

$$x'' + w^2 x=n$$

$w=1$, $x(0)=1$, $n$ is Gaussian noise with mean $0$ and standard deviation of $1$.

Without the Gaussian noise, i can easily solve the equation numerically by using ODE45 in matlab.The problem is, how can i deal with this equation when the Gaussian noise is taken into consideration?

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    Should the equation be $$x''+w^2 x=n$$ or $$x''+w^{2x}=n$$?2012-04-29
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    The first one..sorry i didn't noticed it before2012-04-29
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    In general, you need to find the corresponding [Fokker-Plank equation](http://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation) for the density function. Some details and references can be found, e.g., in the book [The noisy oscillator: The first hundred years](http://www.amazon.com/The-Noisy-Oscillator-Hundred-Einstein/dp/9812565124)2012-04-29
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    Basically, what i need to do is to simulate the equation numerically without having to convert it to its correspondences Fokker-Planck equation..because in my real project, i will have to solve a system of stochastic equations derived from Fokker-Planck equation by using Phase Space representation..but for now, the basic is for me to simulate this equation. any other ideas?2012-04-29

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