Ambit fields: survey and new challenges

2014/05/07 by Mark Podolskij, Podolskij, Mark
Mathematics · #60F05 #60G22 #60G57 #60H05 #60H07 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F05 #msc:60G22 #msc:60G57 #msc:60H05 #msc:60H07

paper · pdf · doi:10.48550/arxiv.1405.1531

1 figure

arxiv created 2014/05/07 · arxiv updated 2014/05/08

Abstract

In this paper we present a survey on recent developments in the study of ambit fields and point out some open problems. Ambit fields is a class of spatio-temporal stochastic processes, which by its general structure constitutes a flexible model for dynamical structures in time and/or in space. We will review their basic probabilistic properties, main stochastic integration concepts and recent limit theory for high frequency statistics of ambit fields.

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