The authors prove central limit theorems for shot noise generated by a stationary multi-dimensional marked point process which is Brillinger mixing. The shot noise has the form \(v(t)=\sum f(t-x_ i,\beta_ i)\), where \(\{x_ i\}\) is the point process, the \(\beta_ i\) are iid marks, and f(\(\cdot)\) is real. Using cumulants of v(\(\cdot)\), it is shown that an appropriately normalized version converges weakly to the Gaussian distribution as the point process intensity \(\lambda\) tends toward infinity.
Similar results are obtained for the integral of v(\(\cdot)\) over a Borel set A, where the product of \(\lambda\) and the measure of A tend towards infinity. Here the authors are able to bound the rate of convergence, and to obtain even sharper results if \(\{x_ i\}\) is a Poisson process. Further results are also obtained for convergence of a random field to the normal.