Ambit fields: survey and new challenges

TL;DR

This paper surveys recent advances in ambit fields, a flexible class of spatio-temporal stochastic processes, highlighting their properties, stochastic integration, and recent limit theory developments.

Contribution

It provides a comprehensive overview of ambit fields, discusses open problems, and introduces new challenges in their study.

Findings

Review of probabilistic properties of ambit fields

Discussion of stochastic integration concepts

Recent limit theory results for high-frequency statistics

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.