{"id":{"repo_id":"qucosa-diss","oai_identifier":"oai:qucosa:de:qucosa:23843"},"canonical_url":"https://search.dev.ndltd.org/etd/qucosa-diss/oai:qucosa:de:qucosa:23843","repository":{"repo_id":"qucosa-diss","name":"QUCOSA","base_url":"http://www.qucosa.de/oai/"},"display":{"title":"The Symbol of a Markov Semimartingale","abstract":"We prove that every (nice) Feller process is an It^o process in the sense of Cinlar, Jacod, Protter and Sharpe (1980). Next we generalize the notion of the symbol and define it for this larger class of processes. As examples the solutions of stochastic differential equations are considered. The symbol is then used to derive a quick approach to the semimartingale characteristics as well as the generator of the process under consideration. Finally we give some examples of how our methods work for processes used in mathematical finance.","abstract_html":"We prove that every (nice) Feller process is an It^o process in the sense of Cinlar, Jacod, Protter and Sharpe (1980). Next we generalize the notion of the symbol and define it for this larger class of processes. As examples the solutions of stochastic differential equations are considered. The symbol is then used to derive a quick approach to the semimartingale characteristics as well as the generator of the process under consideration. Finally we give some examples of how our methods work for processes used in mathematical finance.","abstract_has_math":false,"creators":["Schnurr, Alexander"],"institution":"Technische Universität Dresden","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Schilling, René L.","Nollau, Volker","Jacob, Niels"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-04-27","date_published":"2009-04-27","updated_at":"2026-07-24T03:56:55Z","subjects":["Markov process","semimartingale","Itô process","Feller semigroup","generator","symbol","pseudo differential operator","stochastic differential equation","COGARCH process","Markov Prozess","Semimartingal","Itô Prozess","Feller Halbgruppe","Erzeuger","Pseudo-Differential-Operator","stochastische Differentialgleichung","COGARCH Prozess"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Schilling, René L.","Nollau, Volker","Jacob, Niels"]},{"key":"dc:creator","label":"Author","values":["Schnurr, Alexander"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden","Technische Universität Dresden"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Technische Universität Dresden"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Markov process","semimartingale","Itô process","Feller semigroup","generator","symbol","pseudo differential operator","stochastic differential equation","COGARCH process","Markov Prozess","Semimartingal","Itô Prozess","Feller Halbgruppe","Erzeuger","Pseudo-Differential-Operator","stochastische Differentialgleichung","COGARCH Prozess"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We prove that every (nice) Feller process is an It^o process in the sense of Cinlar, Jacod, Protter and Sharpe (1980). Next we generalize the notion of the symbol and define it for this larger class of processes. As examples the solutions of stochastic differential equations are considered. The symbol is then used to derive a quick approach to the semimartingale characteristics as well as the generator of the process under consideration. Finally we give some examples of how our methods work for processes used in mathematical finance.","Wir haben gezeigt, dass jeder (nette) Feller Prozess ein It^o Prozess im Sinne von Cinlar, Jacod, Protter und Sharpe (1980) ist. Es stellt sich heraus, dass man den Begriff des Symbols, der für Feller Prozesse bekannt ist, auf diese größere Klasse verallgemeinern kann. Dieses Symbol haben wir für die Lösungen verschiedener stochastischer Differentialgleichungen berechnet. Außerdem haben wir gezeigt, dass das Symbol einen schnellen Zugang zur Berechnung der Semimartingal-Charakteristiken und des Erzeugers eines It^o Prozesses liefert. Zuletzt wurden die Ergebnisse auf Prozesse angewendet, die in der Finanzmathematik gebräuchlich sind. - (Die Dissertation ist veröffentlicht im Shaker Verlag GmbH, Postfach 101818, 52018 Aachen, Deutschland, http://www.shaker.de, ISBN: 978-3-8322-8244-8)"]},{"key":"dc:title","label":"Title","values":["The Symbol of a Markov Semimartingale"]}]}],"canonical_facts":{"dc:contributor":["Schilling, René L.","Nollau, Volker","Jacob, Niels"],"dc:creator":["Schnurr, Alexander"],"dc:description.abstract":["We prove that every (nice) Feller process is an It^o process in the sense of Cinlar, Jacod, Protter and Sharpe (1980). Next we generalize the notion of the symbol and define it for this larger class of processes. As examples the solutions of stochastic differential equations are considered. The symbol is then used to derive a quick approach to the semimartingale characteristics as well as the generator of the process under consideration. Finally we give some examples of how our methods work for processes used in mathematical finance.","Wir haben gezeigt, dass jeder (nette) Feller Prozess ein It^o Prozess im Sinne von Cinlar, Jacod, Protter und Sharpe (1980) ist. Es stellt sich heraus, dass man den Begriff des Symbols, der für Feller Prozesse bekannt ist, auf diese größere Klasse verallgemeinern kann. Dieses Symbol haben wir für die Lösungen verschiedener stochastischer Differentialgleichungen berechnet. Außerdem haben wir gezeigt, dass das Symbol einen schnellen Zugang zur Berechnung der Semimartingal-Charakteristiken und des Erzeugers eines It^o Prozesses liefert. Zuletzt wurden die Ergebnisse auf Prozesse angewendet, die in der Finanzmathematik gebräuchlich sind. - (Die Dissertation ist veröffentlicht im Shaker Verlag GmbH, Postfach 101818, 52018 Aachen, Deutschland, http://www.shaker.de, ISBN: 978-3-8322-8244-8)"],"dc:publisher":["Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden","Technische Universität Dresden"],"dc:subject":["Markov process","semimartingale","Itô process","Feller semigroup","generator","symbol","pseudo differential operator","stochastic differential equation","COGARCH process","Markov Prozess","Semimartingal","Itô Prozess","Feller Halbgruppe","Erzeuger","Pseudo-Differential-Operator","stochastische Differentialgleichung","COGARCH Prozess"],"dc:title":["The Symbol of a Markov Semimartingale"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Technische Universität Dresden"]},"updated_at":"2026-07-24T03:56:55Z"}