Tempered operator scaling stable random fields

The content of the new research results are displayed in the chapters three, four and five and follow an introduction in chapter one as well as a repetition and a provision of basics in chapter two. The main objects throughout the dissertation are two special representations of scalar random fields, namely the moving average and the harmonizable representation. We were able to add a tempering to the already known integrand of the operator scaling stable random fields, which allows us to define several new random fields in chapter three. Moreover, the chapters four and five cover an application of the known generalization of stable random fields by adding a dependence on time or place of the stable parameter alpha onto our new fields. Furthermore, we were able to show properties like stochastic continuity and stationary increments as well as explicit elements of tangent field space for the representations. Last but not least, the new tempering allowed a definition of an isolated random field which differs from the other mentioned ones by stationary.