AR Dr. Alexander Schnurr Technische Universität Dortmund Fakultät für Mathematik Vogelpothsweg 87 D-44227 Dortmund Germany

room: phone: fax: email:

M 625 0049-231-755-3099 0049-231-755-3064 Alexander.Schnurr {@}math.tu-dortmund.de

Teaching

Eigenverantwortliche Lehrveranstaltungen / On My Own Responsibility

• SoSe13: Statistik B für BWL (Service Vorlesung / lecture, Siegen)
• SoSe13: Itô Kalkül für allgemeine Semimartingale (Vorlesung / lecture, Siegen)
• SoSe13: Klassische Probleme der Stochastik für die Schule (Seminar /seminar, Siegen)
• WS12/13: Höhere Mathematik I (für ET/IT/AIT/AI) (Service Vorlesung / lecture)
• SoSe12: Sprungprozesse und stochastische Differentialgleichungen (Vorlesung / lecture)
• SoSe12: Wirtschaftsmathematisches Praktikum (practical exercise)
• WS11/12: Klassische Probleme der Stochastik für die Schule (Seminar /seminar)
• WS11/12: Statistische Methoden für Lehramtsstudierende (Seminar /seminar)
• SoSe11: Lévy Prozesse (Vorlesung / lecture)
• SoSe08: Stochastische Modellierung in R (Praktikum / practical exercise, Marburg)

Übungsgruppen / Exercise Groups

• Stochastik I und II, Stochastik für Informatiker (Dortmund)
• Versicherungsmathematik-Seminar, Maßtheorie und Stochastik (Dresden)
• Stochastik 0 bis III, Mathematische Statistik, Mathematik III für Informatiker (Marburg)

Research Interests and Third-Party Funds

Interessensgebiete / Interests

• Semimartingales, Characteristics, SDEs
  
• Markov processes (Hunt, It\^o, Feller, L\'evy)
• Continuous negative definite functions in the sense of Schoenberg
  
• Fine properties of stochastic processes
• Statistics of stochastic volatility models

Drittmittel / Third-Party Funds

• My DFG-funded Project 'Symbole und Indizes in der Theorie der stochastischen Prozesse und ihre Beziehungen zu Feineigenschaften der Trajektorien', page.
• DFG-SFB 823 (Grundausstattung am Lehrstuhl Woerner, Projekt C5: 'Statistik komplexer stochastischer Modelle in der Finanzmathematik'), page.

Publications

Articles and Preprints

• [12] Criteria for the Finiteness of the $p$-Variation (with Martynas Manstavicius). preprint.
• [11] A Criterion for Invariant Measures Based on the Symbol (with Anita Behme). preprint.
• [10] An Ordinal Pattern Approach to Detect and to Model Leverage Effects and Dependence Structures Between Financial Time Series. to appear in Stat. Papers (2013+).
• [9] On Deterministic Markov Processes: Expandability and Related Topics. to appear in Markov Process. Related Fields (2013+).
• [8] Generalization of the Blumenthal-Getoor Index to the Class of Homogeneous Diffusions With Jumps and Some Applications. to appear in Bernoulli (2012+, online).
• [7] On the Semimartingale Nature of Feller Processes with Killing. Stoch. Proc. Appl. 122 (2012), 2758-2780. pdf.
• [6] SDEs Driven by SDE Solutions. Univ. J. Math. and Math. Sci. 1(2) (2012), 83-105. pdf.
• [5] COGARCH: Symbol, Generator and Characteristics. Proceedings of the 8th international Congress of the ISAAC (2011).
• [4] Well-balanced Levy Driven Ornstein-Uhlenbeck Processes (with Jeannette Woerner). Statistics & Risk Modeling 28 (2011), 343–357. pdf.
• [3] A Classification of Deterministic Hunt Processes With Some Applications. Markov Process. Related Fields. 17(2) (2011), 259-276. pdf.
• [2] The Euler Scheme for Feller Processes (with Björn Böttcher). Stochastic Anal. Appl. 29(6) (2011), 1045-1056. pdf.
• [1] The Symbol Associated With the Solution of a Stochastic Differential Equation (with Rene Schilling). Electr. J. Probab. 15 (2010), 1369-1393. pdf.

Theses

• The Symbol of a Markov Semimartingale. PhD thesis, TU Dresden, 2009. Shaker Verlag, Aachen.
• Zeitreihen und hilbertsche Zerlegungen ihrer Prozesskerne.  Staatsexamensarbeit, Uni Marburg, Dez 2005.

Referee

• Stochastic Processes and Their Applications
• Bernoulli
• Markov Processes and Related Fields
• Journal of Mathematical Analysis and Applications
• Scandinavian Journal of Statistics
• Computational Statistics and Data Analysis
• Zentralblatt MATH
  

Some Talks and Posters

• 06.06.2013 (talk): 'Path Properties of Stochastic Processes with Underlying Lévy Dynamics' (German-Polish Stochastic Days, Torun, Poland)
• 17.04.2013 (talk): 'An Ordinal Pattern Approach to Detect and to Model Leverage Effects and Dependence Structures Between Financial Time Series' (DynStoch-Meeting, Copenhagen, Denmark)
• 13.03.2013 (invited talk): 'Blumenthal-Getoor-Indices for Homogeneous Diffusions with Jumps' (Sem. Finance and Insurance Math., Vilnius, Lithuania)
• 12.03.2013 (invited talk): 'Blumenthal-Getoor-Indices for Homogeneous Diffusions with Jumps' (Sem. Prob. Theory and Math. Stat., Vilnius, Lithuania)
• 15.01.2013 (invited talk): 'Quo vadis Symbol (et ubi venis)?' (Duisburg-Essen)
• 06.12.2012 (invited talk): 'Verallgemeinerungen des Blumenthal-Getoor-Index und ihre Anwendungen' (CAU Kiel)
• 22.11.2012 (invited talk & Lehrprobe): 'Kenngrößen stochastischer Prozesse und ihre Beziehung zu Feineigenschaften der Trajektorien' (Marburg)
• 15.11.2012 (talk): 'Studying Stochastic Processes by Using Their Symbol' (Welsh Probability Seminar, Swansea University, Wales)
• 13.07.2012 (talk): 'On a Generalization of the Blumenthal-Getoor Index' (8th World Congress in Probability and Statistics, Istanbul, Turkey)
• 20.06.2012 (invited talk): 'Fine Properties of Stochastic Processes Used in Mathematical Finance' (Oberseminar Wahrscheinlichkeitstheorie, TU & LMU München)
• 07.06.2012 (poster): 'Generalized Blumenthal-Getoor Indices and Some Applications' (DynStoch-Meeting, Institut Henri Poincaré, Paris, France)
• 27.03.2012 (invited talk): 'Some Remarks on Feller Semimartingales and Their Symbols' (Michigan State University, USA)
• 08.03.2012 (talk): 'The Semimartingale Perspective on a Class of Feller Processes with Killing' (Stochastik Tage 2012, Mainz)
• 30.11.2011 (invited talk): 'Well-balanced Lévy Driven OU Processes: Properties and Applications' (TU Kaiserslautern)
• 24.08.2011 (invited talk): 'On the Semimartingale Nature of Feller Processes with Killing' (ISSAC VIII, People's Friendship Univ. Moscow, Russia)
• 17.06.2011 (invited talk): 'Modelling Financial Data With Continuous Time Moving Average Processes' (DynStoch-Meeting, Heidelberg)
• 24.03.2011 (invited talk): 'Some Nice (Counter-)Examples in the Context of Feller and Ito Processes' (Thiele Center Aarhus, Denmark)
• 15.03.2011 (invited talk): 'Fixed Times of Discontinuity and Jump Structures' (Workshop: Analysis of Jump Processes, Bielefeld)
• 04.03.2011 (invited talk): 'A Classification of Deterministic Hunt Processes' (TU Wroclaw, Poland)
• 08.02.2011 (invited talk): 'On a well-balanced Levy driven Ornstein-Uhlenbeck process' (TU Braunschweig)
• 11.01.2011 (invited talk): 'On the Construction of a Hunt Semimartingale which is not an Ito Process' (TU Dresden)
• 14.10.2010 (poster): 'Inference for Semimartingale Stochastic Volatility Models' (Begehung der DFG-FOR 916, Göttingen)
• 09.09.2010 (talk): 'The Symbol of an Ito Process and its Relations to Fine Properties' (Stochastic Processes and Their Applications 2010, Osaka, Japan)
• 26.07.2010 (poster): 'Fine Properties of Processes Given as Solutions of Levy Driven SDEs' (Levy Processes VI, Dresden) 
• 16.07.2010 (invited talk):  'The Symbol of an Ito Process and its Relations to Fine Properties (extended version)' (Siegen)
• 18.06.2010 (talk): 'The Symbol of an Ito Process and its Relations to Fine Properties' (DynStoch-Meeting, Angers, France)
• 03.03.2010 (talk): 'Generalized Indices and Fine Properties of Stochastic Processes' (Stochastik Tage 2010, Leipzig)
• 30.11.2009 (invited talk): 'A New Approach to the Analysis of Markov Semimartingales' (Workshop: Fine Properties of Stochastic Processes, Bielefeld)
• 05.11.2009 (invited talk): 'A New Approach to the Analysis of Markov Semimartingales' (Oberseminar Finanz- und Versicherungsmathematik, TU & LMU München)
• 30.07.2009 (poster): 'A New Approach to the Analysis of Markov Semimartingales' (Stochastic Processes and Their Applications 2009, Berlin)
• 25.06.2009 (talk): 'Das Symbol eines Markov Semimartingals' (Dortmund)
• 27.04.2009 (talk): Disputationsvortrag an der TU Dresden 
• 22.09.2008 (talk): 'Transformed Process and Transformed Symbol' (Stochastic Analysis and Related Topics 3, Dresden)
• 08.04.2008 (invited talk): 'COGARCH: Symbol und Erzeuger' (Interdisziplinäres Statistik-Kolloquium, Marburg / Gießen) 
• 05.03.2008 (talk): 'A Generalized Symbol in the Theory of Stochastic Processes' (Stochastik Tage 2008, Aachen)
• 13.08.2007 (poster): 'The Symbol of a Markov Semimartingale and some Applications' (Lévy Processes V, Copenhagen, Denmark)
• 17.04.2007 (talk): 'The Symbol Associated to the Solution of an SDE' (British Mathematical Colloquium 2007, Swansea, Wales)
  

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