SDEs driven by VMLV processes and ambit fields - A study of existence and uniqueness

Abstract

The main topic of this thesis is SDEs driven by VMLV and VMBV processes. Further study is done on their respective subclasses of processes, abbreviated as LSS and BSS processes. Secondarily, SPDEs driven by ambit fields in an infinite-dimensional Hilbert space are studied. In both cases, the aim is to find conditions ensuring the existence and uniqueness of solutions. Moreover, processes abbreviated as fBSS processes are analyzed. This is (to my knowledge) a new process in the sense that it is defined in this thesis. We also look at SDEs driven by such fBSS processes and attempt to define integrals where the integrator is a fBSS process. Finally, some properties of integrals against VMLV and VMBV processes and ambit fields are obtained.