Some investigations on Feller processes generated by pseudo-differential operators

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 idea...

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Main Author: Bottcher, Bjorn
Published: Swansea University 2004
Online Access:https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.751956
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spelling ndltd-bl.uk-oai-ethos.bl.uk-7519562018-10-09T03:22:41ZSome investigations on Feller processes generated by pseudo-differential operatorsBottcher, Bjorn2004Introducing 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.Swansea University https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.751956https://cronfa.swan.ac.uk/Record/cronfa42541Electronic Thesis or Dissertation
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description 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.
author Bottcher, Bjorn
spellingShingle Bottcher, Bjorn
Some investigations on Feller processes generated by pseudo-differential operators
author_facet Bottcher, Bjorn
author_sort Bottcher, Bjorn
title Some investigations on Feller processes generated by pseudo-differential operators
title_short Some investigations on Feller processes generated by pseudo-differential operators
title_full Some investigations on Feller processes generated by pseudo-differential operators
title_fullStr Some investigations on Feller processes generated by pseudo-differential operators
title_full_unstemmed Some investigations on Feller processes generated by pseudo-differential operators
title_sort some investigations on feller processes generated by pseudo-differential operators
publisher Swansea University
publishDate 2004
url https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.751956
work_keys_str_mv AT bottcherbjorn someinvestigationsonfellerprocessesgeneratedbypseudodifferentialoperators
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