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Space-time models in stochastic geometry. (English) Zbl 1366.60021
Schmidt, Volker (ed.), Stochastic geometry, spatial statistics and random fields. Models and algorithms. Selected papers based on the presentations at the summer academy on stochastic analysis, modelling and simulation of complex structures, Söllerhaus, Hirschegg, Germany, September 11–24, 2011. Cham: Springer (ISBN 978-3-319-10063-0/pbk; 978-3-319-10064-7/ebook). Lecture Notes in Mathematics 2120, 205-232 (2015).
Summary: Space-time models in stochastic geometry are used in many applications. Mostly these are models of space-time point processes. A second frequent situation are growth models of random sets. The present chapter aims to present more general models. It has two parts according to whether the time is considered to be discrete or continuous. In the discrete-time case we focus on state-space models and the use of Monte Carlo methods for the inference of model parameters. Two applications to real situations are presented: a) evaluation of a neurophysiological experiment, b) models of interacting discs. In the continuous-time case we discuss space-time Lévy-driven Cox processes with different second-order structures. Besides the well-known separable models, models with separable kernels are considered. Moreover fully nonseparable models based on ambit processes are introduced. Inference for the models based on second-order statistics is developed.
For the entire collection see [Zbl 1301.60005].

MSC:
60D05 Geometric probability and stochastic geometry
65C60 Computational problems in statistics (MSC2010)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60J22 Computational methods in Markov chains
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