Brownian noise is integration of gaussian or uniform white noise?

Brown noise can be produced by integrating white noise

What kind of white noise is meant? The Gaussian or uniform white noise?

So in the integral defining the Weiner process: $$W(t) = \int_0^t\frac{dW(\tau)}{d\tau}{d\tau}$$
$W(t)$ has samples with Cauchy, Poisson, Gaussian, etc. distributions as long as the power spectral density is uniform, making it white noise.
• I think the OP wanted to ask (or I think the answer should be) is that how different distributions of $W(t)$ does not change the property defining Brownian noise, i.e. $\textrm{PSD} \propto 1/f^2$. – AlexTP May 11 '17 at 16:27