STIT Tessellations -- Ergodic Limit Theorems and Bounds for the Speed of Convergence

Abstract

We consider homogeneous STIT tessellations in the $\ell$-dimensional Euclidean space ${\mathbb{R}}^{\ell }$. Based on results for the spatial $\beta$-mixing coefficient an upper bound for the variance of additive functionals of tessellations is derived, using results by Yoshihara and Heinrich. Moreover, ergodic theorems are applied to subadditive functionals.

References in corpus (1)

• Second-Order Theory for Iteration Stable Tessellations