Abstract:

In the paper asymptotic properties of functionals of stationary Gibbs particle processes are derived. Two known techniques from the point process theory in the Euclidean space $\mathbb{R}^d$ are extended to the space of compact sets on $\mathbb{R}^d$ equipped with the Hausdorff metric. First, conditions for the existence of the stationary Gibbs point process with given conditional intensity have been simplified recently. Secondly, the Malliavin-Stein method was applied to the estimation of Wasserstein distance between the Gibbs input and standard Gaussian distribution. We transform these theories to the space of compact sets and use them to derive a Gaussian approximation for functionals of a planar Gibbs segment process.

Keywords:

asymptotics of functionals, innovation, stationary Gibbs particle process, Wasserstein distance

60D05, 60G55

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