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Some investigations on Feller processes generated by pseudo-differential operators. / Bjorn Bottcher

Swansea University Author: Bjorn Bottcher

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 idea...

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Published: 2004
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42541
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first_indexed 2018-08-02T18:54:57Z
last_indexed 2018-08-03T10:10:25Z
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spelling 2018-08-02T16:24:29.6029952 v2 42541 2018-08-02 Some investigations on Feller processes generated by pseudo-differential operators. 9a287a27d6a19aa25b5904cd2e6f8683 NULL Bjorn Bottcher Bjorn Bottcher true true 2018-08-02 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. E-Thesis Mathematics. 31 12 2004 2004-12-31 COLLEGE NANME Mathematics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:29.6029952 2018-08-02T16:24:29.6029952 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Bjorn Bottcher NULL 1 0042541-02082018162502.pdf 10805290.pdf 2018-08-02T16:25:02.6300000 Output 2283254 application/pdf E-Thesis true 2018-08-02T16:25:02.6300000 false
title Some investigations on Feller processes generated by pseudo-differential operators.
spellingShingle Some investigations on Feller processes generated by pseudo-differential operators.
Bjorn Bottcher
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.
author_id_str_mv 9a287a27d6a19aa25b5904cd2e6f8683
author_id_fullname_str_mv 9a287a27d6a19aa25b5904cd2e6f8683_***_Bjorn Bottcher
author Bjorn Bottcher
author2 Bjorn Bottcher
format E-Thesis
publishDate 2004
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
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.
published_date 2004-12-31T03:53:10Z
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score 10.997933

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