Nonparametric inference for thinned point process

We consider possibly dependent data N-1',...,N-n' of the p-thinning N' of a point process N and construct estimators (p) over cap and (L) over cap of the thinning function p and of the Laplace functional of N. Under mixing conditions we prove the mean square convergence of (p) over cap, the uniform almost sure convergence of (p) over cap and (L) over cap and the asymptotic normality of (p) over cap.