Research

Research interests:

Generally speaking, my research interests can be specified as follows:

• stochastic processes
• stochastic analysis
• stochastic models with a branching structure
• probabilistic models motivated by mathematical finance or population genetics
• martingale theory
• random graphs
• interrelation between probability theory and analysis

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Publications:

• Maximal inequalities for fractional Lévy and related processes (with Christian Bender and Philip Oberacker), Stoch. Anal. Appl., 33 (4), 701-714, 2015, DOI: 10.1080/07362994.2015.1036167

• A generalised Itō formula for Lévy-driven Volterra processes (with Christian Bender and Philip Oberacker), Stochastic Process. Appl., 125 (8), 2989-3022, 2015, DOI: 10.1016/j.spa.2015.02.009

• The Kingman tree length process has infinite quadratic variation (with Iulia Dahmer and Anton Wakolbinger), Electron. Comm. Probab., 19 (87), 12 pp, 2014, DOI: 10.1214/ECP.v19-3318

• Survival of homogeneous fragmentation processes with killing (with A. E. Kyprianou), Ann. Inst. H. Poincaré Probab. Statist., 50 (2), 476-491, 2014, DOI: 10.1214/12-AIHP520

• Strong law of large numbers for fragmentation processes (with S. C. Harris and A. E. Kyprianou), Ann. Inst. H. Poincaré Probab. Statist., 46 (1), 119-134, 2010, DOI: 10.1214/09-AIHP311

• Uniform conditional ergodicity and intrinsic ultracontractivity (with L. Partzsch), Potential Anal., 33 (2), 107-136, 2010, DOI: s11118-009-9161-5

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Preprints:

• Asymptotic properties of the process counted with a random characteristic in the context of fragmentation processes, arXiv: 1203.4212

• Limit theorems for fragmentation processes with immigration, arXiv: 1204.5142

• One-sided FKPP travelling waves in the context of homogenous fragmentation processes, arXiv: 1204.0758

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Theses:

• Asymptotic properties of fragmentation processes, PhD thesis, University of Bath, January 2011

• Intrinsic ultracontractivity and uniform conditional ergodicity, Diplom thesis, TU Dresden, May 2007

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Research talks:

• 06.12.2015: Applications of random characteristics in the context of fragmentation processes, 2015 CMS Winter Meeting, Montreal, Quebec (Canada), invited talk (on invitation by Prof. Xiaowen Zhou, Concordia University)

• 01.07.2015: A generalised Itō formula for Lévy-driven Volterra processes, 2015 IMS-China International Conference on Statistics and Probability, Kunming, Yunnan (China)

• 28.04.2014: Asymptotic properties of fragmentation processes with killing, Seminar, Lancaster University (UK)

• 07.03.2014: Limit theorems for fragmentation processes with immigration, 11th German probability and statistics days, Universität Ulm (Germany)

• 10.02.2014: An Itō type formula and related properties for convoluted Lévy processes, Seminario di probabilità e statistica, Università degli Studi di Torino (Italy)

• 23.01.2014: An Itō type formula for convoluted Lévy processes, Oberseminar Stochastik, TU Darmstadt (Germany)

• 09.07.2013: A strong law of large numbers for the fragmentation energy model, Summer school on Lévy processes, Mathematical Research and Conference Center, Będlewo (Poland)

• 20.06.2013: An Itō formula for convoluted Lévy processes - The L^2-case, Stochastics research seminar, Universität des Saarlandes (Germany)

• 22.02.2013: Limit theorems for random characteristics associated with fragmentation processes, 3rd PL^2US workshop, Universität des Saarlandes (Germany)

• 31.01.2013: Asymptotic properties of fragmentation processes with killing, Seminar, Westfälische Wilhelms-Universität Münster (Germany)

• 17.09.2012: Limit theorems for random characteristics associated with fragmentation processes, Annual Meeting of the German Mathematical Society, Universität des Saarlandes (Germany)

• 27.06.2012: The FKPP equation in the context of fragmentation processes with killing, Seminar, Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany)

• 25.06.2012: Asymptotic properties of fragmentation processes with killing, Stochastics research seminar, Universität des Saarlandes (Germany)

• 06.06.2012: Survival of fragmentation processes with killing, Seminar, Université d'Aix-Marseille (France)

• 03.05.2012: Killed fragmentations and the FKPP equation, Stochastic Colloquium, Georg-August-Universität Göttingen (Germany)

• 06.03.2012: Asymptotic properties of the process counted with a random characteristic in the context of fragmentation processes, 10th German probability and statistics days, Johannes Gutenberg Universität Mainz (Germany)

• 23.01.2012: Survival of fragmentation processes with killing, Seminar, TU München (Germany)

• 08.09.2011: Random characteristics associated with fragmentation processes, Frankfurt Seminar on random discrete structures, Goethe Universität Frankfurt am Main (Germany)

• 06.08.2010: Martingales associated with killed fragmentation processes, Stochastik-Kolloquium, Goethe Universität Frankfurt am Main (Germany)

• 24.07.2010: Killed fragmentations and intrinsic spectrally negative Lévy processes, Summer school on Lévy processes, TU Braunschweig (Germany)

• 20.07.2010: Martingales associated with killed fragmentation processes, Probability at Warwick young researchers workshop, University of Warwick (UK)

• 27.05.2010: One-sided FKPP travelling waves for fragmentation processes, Colloquium, University of Bath (UK)

• 19.05.2010: Fragmentation processes and the FKPP equation, Prob-L@B seminar, University of Bath (UK)

• 27.07.2009: Strong law of large numbers for fragmentation processes with immigration, 33rd conference on stochastic processes and their applications, TU Berlin (Germany)

• 25.03.2009: Strong law of large numbers for fragmentation processes with immigration, YEP 2009 - workshop on fragmentation, coalescence and probabilistic genetics, EURANDOM (Eindhoven, the Netherlands)

• 16.01.2009: Strong law of large numbers for fragmentation processes, Jumps 2009 - workshop on jump processes, TU Dresden (Germany)

• 09.01.2009: Strong law of large numbers for fragmentation processes, Seminario di probabilità, Sapienza - Università di Roma (Italy)

• 17.06.2008: Strong law of large numbers for fragmentation processes, PIMS summer school in probability, UBC Vancouver (Canada)

• 13.05.2008: Some limit theorems for homogeneous fragmentation processes, graduate course: Fragmentation and coagulation processes, University of Bath (UK)

• 05.03.2008: Uniform conditional ergodicity and intrinsic ultracontractivity, 8th German probability and statistics days, RWTH Aachen (Germany)

• 12.12.2007: Uniform conditional ergodicity and intrinsic ultracontractivity, Prob-L@B seminar, University of Bath (UK)

• 15.06.2007: Intrinsic Ultracontractivity and Uniform Conditional Ergodicity, Institutsseminar Stochastik, TU Dresden (Germany)

• 29.03.2007: Intrinsic Ultracontractivity and Uniform Conditional Ergodicity, Oberseminar Stochastik, Universität Bonn (Germany)

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Research posters:

• 15.07. - 19.07.2013: An Itō formula for convoluted Lévy processes, 7th International conference on Lévy processes: theory and applications, University of Wrocław (Poland)
• 26.07. - 30.07.2010: Killed fragmentations and intrinsic spectrally negative Lévy processes, 6th International conference on Lévy processes: theory and applications, TU Dresden (Germany)
• 20.07. - 24.07.2009: Strong law of large numbers for fragmentation processes, International conference on selfsimilar processes and their applications, Université d'Angers (France)