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Probability and Heat Kernel Estimates for Lévy(-Type) ProcessesKühn, Franziska 05 December 2016 (has links) (PDF)
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.
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Probability and Heat Kernel Estimates for Lévy(-Type) ProcessesKühn, Franziska 25 November 2016 (has links)
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.
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