Metatimes, random measures and cylindrical random variables

Metatimes constitute an extension of time-change to general measurable spaces, defined as mappings between two σ-algebras. Equipping the image σ-algebra a metatime with measure and defining composition given by on domain σ-algebra, we identify metatimes bounded linear operators spaces square integrable functions. We also analyse possibility define from operator Hilbert which show is possible for invertible operators. Next establish link orthogonal random measures cylindrical variables following classical construction. This enables us view metatime-changed composed operators, where are induced metatimes. In paper provide several results basic properties well some applications towards trawl processes.