Probability and Heat Kernel Estimates for Lévy(-Type) Processes

Franziska Kühn

AutorIn

Franziska Kühn

Titel

Probability and Heat Kernel Estimates for Lévy(-Type) Processes

Zitierfähige Url:

https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa-214839

Datum der Einreichung

12.07.2016

Datum der Verteidigung

25.11.2016

Abstract (EN)

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.

Freie Schlagwörter (DE)

Wahrscheinlichkeitstheorie, Lévy-typ Prozess, Feller Prozess, Lévy Prozess, Parametrix-Konstruktion, Momente, stochastische Differentialgleichungen, Existenz, stable-like

Freie Schlagwörter (EN)

probability theory, Lévy-type processes, Feller processes, Lévy processes, parametrix construction, stochastic differential equation, moments, existence result, stable-like, heat kernel estimates

Klassifikation (DDC)

510

Klassifikation (RVK)

SK 820

Normschlagwörter (GND)

Wahrscheinlichkeitstheorie

GutachterIn