A representation of infinitely divisible signed random measures.
Histogrammes, noyaux et densités irrégulières
Représentations convergentes des intégrales stochastiques
Extreme values and kernel estimates of point processes boundaries
We present a method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on a Parzen-Rosenblatt kernel and extreme values of point processes. We give conditions for various kinds of convergence and asymptotic normality. We propose a method of reducing the negative bias and edge effects, illustrated by some simulations.
Extreme values and kernel estimates of point processes boundaries
We present a method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on a Parzen-Rosenblatt kernel and extreme values of point processes. We give conditions for various kinds of convergence and asymptotic normality. We propose a method of reducing the negative bias and edge effects, illustrated by some simulations.
Stability of extreme value for a multidimensional sample
Mean quadratic convergence of signed random measures
We consider signed Radon random measures on a separable, complete and locally compact metric space and study mean quadratic convergence with respect to vague topology on the space of measures. We prove sufficient conditions in order to obtain mean quadratic convergence. These results are based on some identification properties of signed Radon measures on the product space, also proved in this paper.
On the conditional intensity of a random measure
We prove the existence of the conditional intensity of a random measure that is absolutely continuous with respect to its mean; when there exists an L-intensity, , the conditional intensity is obtained at the same time almost surely and in the mean.
Page 1