Ambit Processes and Stochastic Partial Differential Equations

Abstract

Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis.

Keywords: Ambit processes, stochastic partial differential equations, Lévy bases, Lévy noise, Walsh theory of martingale measures, turbulence, finance

JEL Classification: C0, C1, C5