Titlebook: Ambit Stochastics; Ole E. Barndorff-Nielsen,Fred Espen Benth,Almut E. Book 2018 Springer Nature Switzerland AG 2018 60G60, 60F05, 60H05, 6

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Book 2018f ambit fields and a comprehensive stochastic integration theory for Volterra processes in a non-semimartingale context...Written by pioneers in the subject, this book will appeal to researchers and graduate students interested in empirical stochastic modelling..

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Thorsten Kuthe,Madeleine Zipperlethod is based on a particular series expansion of the ambit field along a set of basis functions. We expand on this idea and view ambit fields as stochastic processes in a separable Hilbert space, where we establish a series representation of the fields as a countable sum of volatility modulated Volterra processes scaled by basis functions.

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Trawl Processesic processes in time, where the temporal dependence structure is specified through the ambit sets. An application to high-frequency financial time series data demonstrates the flexibility and attractiveness of trawl processes.

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Simulation transform, where we express the kernel function in the volatility modulated Volterra process along a basis so that the simulation task essentially becomes a summation of a weighted series of complex-valued Ornstein-Uhlenbeck processes. In some cases we can use the Laplace transform instead, providi

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Asymptotic Theory for Power Variation of LSS Processesiation techniques are used to draw inference on the integrated variance process. The theory is rather well-developed for semimartingales, in particular for the Brownian case, but some theory can also be developed for Lévy-driven models. Beyond the semimartingale framework, the asymptotic theory for