DanJW
asked on
Convolution of Two Gaussians is a Gaussian
Hey, I'm looking for a proof of this
int G(y-a,sig1)G(y-b,sig2)dy = G(a-b,sig1+sig2)
where G(y-x,sig) is a gaussian with covariance matrix sig and vector y-x.
Or in words, the proof that the convolution of two gaussians centered at a and b is a gaussian centered on a-b with covariance equal to sig1 + sig2
int G(y-a,sig1)G(y-b,sig2)dy = G(a-b,sig1+sig2)
where G(y-x,sig) is a gaussian with covariance matrix sig and vector y-x.
Or in words, the proof that the convolution of two gaussians centered at a and b is a gaussian centered on a-b with covariance equal to sig1 + sig2
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