David Kramer-Bang
I am a fourth-year PhD student in the Warwick Maths and Stats CDT programme at the Department of Statistics of the University of Warwick under the supervision of Professor Aleksandar MijatovićLink opens in a new window. My main interests are in applied and theoretical probability. Currently, my main area of research is on Lévy processes and concave majorants (convex minorants).
Publications and preprints:
Title: Hölder continuity of the convex minorant of a Lévy process
Authors: David Bang, Jorge Ignacio González Cázares & Aleksandar Mijatović.
Preprint, 2022. Link: arXivLink opens in a new window, ResearchGateLink opens in a new window.
Title: How smooth can the convex hull of a Lévy path be?
Authors: David Bang, Jorge Ignacio González Cázares & Aleksandar Mijatović.
Preprint, 2022. Link: arxivLink opens in a new window, ResearchGateLink opens in a new window.
Title: When is the convex hull of a Lévy path smooth?
Authors: David Bang, Jorge Ignacio González Cázares & Aleksandar Mijatović.
Accepted to appear in Annales de l'Institut Henri Poincaré, 2023. Link: arxivLink opens in a new window, ResearchGateLink opens in a new window.
Title: Asymptotic shape of the concave majorant of a Lévy process
Authors: David Bang, Jorge Ignacio González Cázares & Aleksandar Mijatović.
Published in Annales Henri Lebesgue, Volume 5 (2022), pp. 779-811. Link: arxivLink opens in a new window, ResearchGateLink opens in a new window.
Title: A Gaussian approximation theorem for Lévy processes
Authors: David Bang, Jorge Ignacio González Cázares & Aleksandar Mijatović.
Published in "Statistics & Probability Letters", issue 178, 2021. Link: arXivLink opens in a new window, ResearchGateLink opens in a new window.
Talks at conferences and workshops:
1st June 2023: Coupling of multidimensional Lévy processes and Wasserstein bounds in the small-time stable domain of attraction, Invited speaker at Random Models workshop hosted by Aarhus University, Sandbjerg Estate (DK).
16th July 2022: When is the convex hull of a Lévy path smooth?, Contributed talk at Summer SchoolLink opens in a new window of 10th International Conference on Lévy ProcessesLink opens in a new window, Mannheim (Germany).
29th June 2022: How smooth can the convex hull of a Lévy path be?, Invited speaker to session IP20, IMS Annual Meeting 2022Link opens in a new window, London (UK).
21st April 2022: Asymptotic length of the concave majorant of a Lévy process, talk at Isaac Newton Institute for Mathematical Sciences, Optimal control and fractional dynamics Workshop, (FD2W03). The talk can be watched here: https://youtu.be/MT7X3y-ZtJ0?t=2107, Cambridge (UK).
Posters at conferences and workshops:
28th June 2023: How smooth can the convex hull of a Lévy path be?, Presented poster at poster session at "Random Structures, Applied Probability and Computation", a LMS Research School on Probability at the University of Liverpool, UK.
27th October 2022: How smooth can the convex hull of a Lévy path be?, Presented poster at poster session at UCL statistical science poster dayLink opens in a new window (won one of the book prizes for the poster), University College London, UK.
26th July 2022: How smooth can the convex hull of a Lévy path be?, Presented poster at poster session of Lévy processes and random walks - A workshop in celebration of Ron Doney's 80th birthday, The University of Manchester, UK.
18th July 2022: How smooth can the convex hull of a Lévy path be?, Presented poster at poster session of 10th International Conference on Lévy ProcessesLink opens in a new window, The University of Mannheim, Germany.
Seminar talks:
13th April 2023: Coupling of multidimensional Lévy processes and Wasserstein bounds in the small-time stable domain of attraction, Stochastics seminarLink opens in a new window, Aarhus University, Denmark.
22nd February 2023: Coupling of multidimensional Lévy processes and Wasserstein bounds in the small time stable domain of attraction, Stochastic Finance seminarLink opens in a new window, University of Warwick.
31st January 2023: Coupling of multidimensional Lévy processes and Wasserstein bounds in the small time stable domain of attraction, YRMLink opens in a new window, University of Warwick.
15th November 2022: When is the convex hull of a Lévy path smooth?, Stochastics seminarLink opens in a new window, Aarhus University, Denmark.
8th November 2022: When is the convex hull of a Lévy path smooth?, Doctoral probability seminarLink opens in a new window, University of Zagreb (Online).
22nd February 2022: When is the convex hull of a Lévy path smooth?, YRMLink opens in a new window, Warwick University.
10th December 2021: Asymptotic length of the concave majorant of a Lévy process, Applied Probability seminar, Warwick University.
28th April 2021: Asymptotic length of the concave majorant of a Lévy process, WOMPS seminarLink opens in a new window, Warwick University.
4th March 2021: Asymptotic length of the concave majorant of a Lévy process, SPAAM seminarLink opens in a new window, Warwick University.
Teaching at Warwick University:
2020/2021 - Term 1: ST208 - Mathematical Methods.
2020/2021 - Term 1: ST218 - Mathematical Statistics Part A.
2021/2022 - Term 1: ST208 - Mathematical Methods.
2021/2022 - Term 1: ST218 - Mathematical Statistics Part A.
2021/2022 - Term 2: ST202 - Stochastic Processes.
2022/2023 - Term 1: ST208 - Mathematical Methods.
2022/2023 - Term 1: ST218 - Mathematical Statistics Part A.
Education:
I have a BSc in Mathematics from Aarhus University and a MSc in Statistics from Aarhus University.
