In this thesis, we present a new existence result for Lévy-type processes. Lévy-type processes behave locally like a Lévy process, but the Lévy triplet may depend on the current position of the process. They can be characterized by their so-called symbol; this is the analogue of the characteristic exponent in the Lévy case. Using a parametrix construction, we prove the existence of Lévy-type processes with a given symbol under weak regularity assumptions on the regularity of the symbol. Applications range from existence results for stable-like processes and mixed processes to uniqueness results for Lévy-driven stochastic differential equations.
Moreover, we discuss sufficient conditions for the existence of moments of Lévy-type processes and derive estimates for fractional moments.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:14-qucosa-214839 |
| Date | 05 December 2016 |
| Creators | Kühn, Franziska |
| Contributors | Technische Universität Dresden, Fakultät Mathematik und Naturwissenschaften, Prof. Dr. René L. Schilling, Prof. Dr. René L. Schilling, Prof. Dr. Alexei Kulik |
| Publisher | Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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