Ambit Stochastics Part I The purely temporal case 1 Volatility modulated Volterra processes 2 Simulation 3 Asymptotic theory for power variation of LSS processes 4 Integration with respect to volatility modulated Volterra processes Part II The spatio temporal case 5 The ambit framework 6 Representation and simulation of ambit fields 7 Stochastic integration with ambit fields as integrators 8 Trawl processes Part III Applications 9 Turbulence modelling 10 Stochastic modelling of energy spot prices by LSS processes 11 Forward curve modelling by ambit fields Appendix A: Bessel functions Appendix B: Generalised hyperbolic distribution References Index 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