Consider two random variables $Z$ and $w$. Given the variances of $Z$ and $w$, how can we compute the variance of their convolution $Z \circledast w $? As an example, please consider the case of noise ($Z$) in an image being modeled by a Gaussian distribution of zero mean and a given variance $\sigma_Z^2$. Suppose we perform a convolution of $Z$ with a Gaussian kernel denoted by $w$. How can we find the variance of $Z \circledast w $? I am not able to find a good reference for this. Thanks for any help.