Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.751956
Title: Some investigations on Feller processes generated by pseudo-differential operators
Author: Bottcher, Bjorn
Awarding Body: University of Wales, Swansea
Current Institution: Swansea University
Date of Award: 2004
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Abstract:
Introducing an appropriate symbolic calculus for non-classical real-valued symbols, so-called negative definite symbols, W. Hoh succeeded to prove that such operators generate often Feller semigroups. In a first part of this thesis we extend this result to complex-valued symbols. Further, using ideas due to H. Kumano-go in case of classical pseudo-differential operators, we construct a parametrix for the fundamental solution of the associated evolution equation, and thus arrive at an approximation for the generated Feller semigroup. Finally, we use this theory to extend models in financial mathematics based on Levy processes. This is done by using the above mentioned results in situations where parameters in characteristic exponents of Levy processes are made state- space dependent. Especially Meixner-type processes are discussed in detail.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.751956  DOI: Not available
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