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Some Recent Developments in Ambit Stochastics

By Ole E. Barndorff-Nielsen, Emil Hedevang, Jürgen Schmiegel and Benedykt Szozda
Thiele Research Reports
No. 03, February 2015

Some of the recent developments in the rapidly expanding field of Ambit Stochastics are here reviewed. After a brief recall of the framework of Ambit Stochastics three topics are considered: (i) Methods of modelling and inference for volatility/intermittency processes and fields (ii) Universal laws in turbulence and finance in relation to temporal processes (iii) Stochastic integration for time changed volatility modulated Levy-driven Volterra processes.

Keywords: ambit stochastics, extended subordination, finance, metatimes, non-semimartingales, stochastic integration, time-change, stochastic volatility/intermittency, turbulence, universality.

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