The new mathematical field of Ambit Stochastic has its origin in the study of turbulence but is in fact of broad applicability in science, technology and finance, in relation to modelling of spatio-temporal dynamic processes.
The particular character of ambit processes has raised a plethora of new, purely mathematical research questions whose solutions are, in particular, essential for the building of a full-fledged stochastic analysis for such processes. A key element in this is the fact that ambit processes are generally not of the semimartingale type. Important related and highly active areas of mathematical research are Malliavin calculus and the theory of stochastic partial differential equations, and Volterra processes.
Talk at the Workshop on Ambit Processes, Non-Semimartingales and Applications, Sandbjerg Estate 2010
