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Space-Time Models in Stochastic Geometry

  • Viktor BenešEmail author
  • Michaela Prokešová
  • Kateřina Staňková Helisová
  • Markéta Zikmundová
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2120)

Abstract

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 wellknown 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.

Keywords

Point Process Intensity Function Sequential Monte Carlo Conditional Intensity Projection Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Viktor Beneš
    • 1
    Email author
  • Michaela Prokešová
    • 1
  • Kateřina Staňková Helisová
    • 2
  • Markéta Zikmundová
    • 1
  1. 1.Charles University in Prague, Faculty of Mathematics and PhysicsPraha 8Czech Republic
  2. 2.Czech Technical University in Prague, Faculty of Electrical EngineeringPraha 6Czech Republic

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