Adding randomness to nonlinear semigroups: existence, uniqueness and asymptotic results
FacultiesFakultät für Mathematik und Wirtschaftswissenschaften
InstitutionsInstitut für Stochastik
The origins of this thesis lie in the present author’s study of the asymptotic behavior of the weighted p-Laplacian evolution equation, which is one of the bench marks of nonlinear evolution equations and used to model many physical phenomena, such as the evolution of fluvial landscapes. Due to these modeling aspects, it is of great interest to add randomness to such an equation. In this thesis, we investigate two different ways of doing that: We literally add a pure-jump noise to a nonlinear semigroup and derive an existence, uniqueness and asymptotic theory for the resulting process; and secondly, we replace the weight function occurring in the p-Laplacian evolution equation by a random quantity. Hereby, the first approach will be set up for arbitrary nonlinear semigroups, and the applicability of our results will be demonstrated at hand of the p-Laplacian evolution equation; and the latter approach is written specifically for the p-Laplacian case.
Subject HeadingsZentraler Grenzwertsatz [GND]
Limit theorems (Probability theory) [LCSH]