Drawing on advanced probability theory, Ambit Stochastics is used to
model stochastic processes which depend on both time and space. This
monograph, the first on the subject, provides a reference for this
burgeoning field, complete with the applications that have driven its
development.
Unique to Ambit Stochastics are ambit sets, which allow the delimitation
of space-time to a zone of interest, and ambit fields, which are
particularly well-adapted to modelling stochastic volatility or
intermittency. These attributes lend themselves notably to applications
in the statistical theory of turbulence and financial econometrics. In
addition to the theory and applications of Ambit Stochastics, the book
also contains new theory on the simulation of 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.