Poisson Hulls


28 квітня 2021 року о 14 год 15 хв

We consider a hull operator on Poisson point processes, the easiest example being the convex hull of the support. Assuming that the intensity measure of the process is known on the set generated by the hull operator, we discuss estimation of the expected symmetric statistics built on the Poisson process. The results are based on a stopping property of this set in relation to the filtration generated by the underlying Poisson process. In special cases, our general scheme yields the estimator of the volume of the convex support or the estimator of an integral of a H\"older function. The setting is extended to higher order symmetric statistics, and it is shown that the estimation error is given by the Kabanov--Skorohod integral with respect to the underlying Poisson process.  We derive the rate of normal convergence for the estimation error, and illustrate it on an application to estimators of integrals of a Hölder function. This is a joint work with Günter Last.

Доповідач: Ilya Molchanov (University of Bern, Switzerland)

Дата проведення: 28 квітня 2021 року о 14 год 15 хв.