Noise sensitivity of Lévy driven SDE’s : estimates and applications

18.07.2017, 10.15  –  Haus 9, Raum 0.13
Forschungsseminar Wahrscheinlichkeitstheorie

Tania Kosenkova (Potsdam)

The topic of this talk is induced by the following question: whether the deviation between the solutions of two different Lévy driven SDE’s can be controlled in terms of the characteristics of the underlying Lévy processes? In the case of SDE’s with additive noise we give the estimate for the deviation between the solutions in terms of the coupling distance for Lévy measures, which is based on the notion of the Wasserstein distance. In case of Lévy-type processes, whose characteristic triplets are state dependent, we exploit the fact that every Lévy kernel can be obtained by means of a certain infinite Lévy measure and the transform function. And under an appropriate set of conditions on the state dependent characteristic triplet the Lévy-type process can be described as a strong solution to a Lévy driven SDE with multiplicative noise. The estimate of the deviation between two Lévy-type processes is given in terms of transportation distance between the Lévy kernels, which uses the transform functions of the kernels. Such estimates can be applied to the analysis of the low-dimensional conceptual climate models with paleoclimate data.