Research
The research of our group focuses on the theoretical and statistical questions for stochastic processes, such as
- stochastic differential equations (with jumps)
- Lévy processes
- branching processes
- self-similar Markov processes
These processes are central in the growth of probability theory during the past decades and have various applications in industry for instance in insurance and banking.
Publications
- Döring, L., Savov, M., Trottner, L. and Watson, A. R. (2024). The uniqueness of the Wiener–Hopf factorisation of Lévy processes and random walks. The Bulletin of the London Mathematical Society, 1–18.
- Döring, L., Gonon, L., Prömel, D. J. and Reichmann, O. (2021). Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker-Planck equations. Journal of Theoretical Probability, 34, 173–205.
- Döring, L. and Kyprianou, A. E. (2020). Entrance and exit at infinity for stable jump diffusions. The Annals of Probability, 48, 1220-1265.
- Döring, L., Kyprianou, A. E. and Weissmann, P. (2020). Stable processes conditioned to avoid an interval. Stochastic Processes and Their Applications, 130, 471–487.
- Döring, L. and Weissmann, P. (2020). Stable processes conditioned to hit an interval continuously from the outside. Bernoulli : Official Journal of the Bernoulli Society for Mathematical Statistics and Probability, 26, 980-1015.
- Döring, L., Gonon, L., Prömel, D. J. and Reichmann, O. (2019). On Skorokhod embeddings and Poisson equations. The Annals of Applied Probability, 29, 2302-2337.
- Döring, L., Watson, A. R. and Weissmann, P. (2019). Levy processes with finite variance conditioned to avoid an interval. Electronic Journal of Probability : EJP, 24, 1–32.
- Döring, L. (2018). Unterschiede von Studierenden als Herausforderung betrachten. Forschung & Lehre, 25, 03.08.2018.
- Dreieich, S., Döring, L. and Kyprianou, A. E. (2017). Real self-similar processes started from the origin. The Annals of Probability, 45, 1952-2003.
- Döring, L., Horvath, B. and Teichmann, J. (2017). Functional analytic (ir-)regularity properties of SABR type processes. International Journal of Theoretical and Applied Finance : IJTAF, 20, 1750013-1-48.
- Döring, L., Klenke, A. and Mytnik, L. (2017). Finite system scheme for mutually catalytic branching with infinite branching rate. The Annals of Applied Probability, 27, 3113-3152.
- Kolb, O., Döring, L., Klinger, M., Schlather, M. and Schmidt, M. U. (2017). Individualisierte Tutorien im Mathematikstudium. Neues Handbuch Hochschullehre, 82, 77–88.
- Döring, L. and Kyprianou, A. E. (2016). Perpetual integrals for Lévy processes. Journal of Theoretical Probability, 29, 1192-1198.
- Berestycki, J., Döring, L., Mytnik, L. and Zambotti, L. (2015). Hitting properties and non-uniqueness for SDEs driven by stable processes. Stochastic Processes and Their Applications, 125, 918–940.
- Döring, L. (2015). A jump-type SDE approach to real-valued self-similar Markov processes. Transactions of the American Mathematical Society, 367, 7797-7836.
- Barczy, M., Döring, L., Li, Z. and Pap, G. (2014). Parameter estimation for a subcritical affine two factor model.
Journal of Statistical Planning and Inference : JSPI, 151/
2, 37–59. - Barczy, M., Döring, L., Li, Z. and Pap, G. (2014). Stationarity and ergodicity for an affine two factor model. Advances in Applied Probability, 46, 878–898.
- Berestycki, J., Döring, L., Mytnik, L. and Zambotti, L. (2014). On exceptional times for generalized Fleming-Viot processes with mutations. Stochastic Partial Differential Equations : Analysis and Computations, 2, 84–120.
- Aurzada, F., Döring, L. and Svavov, M. (2013). Small time Chung-type LIL for Lévy processes. Bernoulli : Official Journal of the Bernoulli Society for Mathematical Statistics and Probability, 19, 115–136.
- Barczy, M. and Döring, L. (2013). On entire moments of self-similar Markov processes. Stochastic Analysis and Applications, 31, 191–198.
- Barczy, M., Döring, L., Li, Z. and Pap, G. (2013). On parameter estimation for critical affine processes. Electronic Journal of Statistics : EJS, 7, 647–696.
- Döring, L. and Barczy, M. (2012). A jump-type SDE approach to positive self-similar Markov processes. Electronic Journal of Probability : EJP, 17, 1–39.
- Döring, L. and Mytnik, L. (2012). Mutually catalytic branching processes and voter processes with strength of opinion. ALEA : Latin American Journal of Probability and Mathematical Statistics, 9, 1–51.
- Aurzada, F. and Döring, L. (2011). Intermittency and ageing for the symbiotic branching model. Annales de l'Institut Henri Poincaré. B, Probabilité et statistiques, 47, 376–394.
- Blath, J., Döring, L. and Etheridge, A. (2011). On the moments and the interface of the symbiotic branching model. The Annals of Probability, 39, 252–290.
- Döring, L. and Svavov, M. (2011). (Non)differentiability and asymptotics for potential densities of subordinators. Electronic Journal of Probability : EJP, 16, 470–503.
- Döring, L. and Svavov, M. (2010). An application of the renewal theorem to exponential moments of local times. Electronic Communications in Probability : ECP, 15, 263–269.
- Döring, L., Gonon, L., Prömel, D. J. and Reichmann, O. (2018). Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker-Planck equations. Mannheim [u.a.].
- Döring, L. and Kyprianou, A. E. (2018). Entrance and exit at infinity for stable jump diffusions. Mannheim [u.a.].
- Döring, L., Kyprianou, A. E. and Weissmann, P. (2018). Stable processes conditioned to avoid an interval. Mannheim [u.a.].
- Döring, L., Watson, A. R. and Weissmann, P. (2018). Lévy processes with finite variance conditioned to avoid an interval. Mannheim [u.a.].
- Döring, L. and Weissmann, P. (2018). Stable processes conditioned to hit an interval continuously from the outside. Mannheim [u.a.].
- Döring, L., Gonon, L., Prömel, D. J. and Reichmann, O. (2017). On Skorokhod embeddings and Poisson equations. Mannheim [u.a.].
- Dreieich, S. and Döring, L. (2014). Random interlacements via Kuznetsov measures. Mannheim [u.a.].
- Döring, L. and Roberts, M. I. (2013). Catalytic branching processes via spine techniques and renewal theory. In , Séminaire de Probabilités XLV (S. 305–322). Lecture Notes in Mathematics, Springer: Berlin ; Heidelberg [u.a.].
- Döring, L. and Mytnik, L. (2013). Longtime behavior of mutually catalytic branching with negative correlations. In Advances in superprocesses and nonlinear PDEs (S. 93–111). Boston, MA [u.a.]: Springer.
- Döring, L. (2009). Fine properties of symbiotic branching processes. Dissertation. Berlin.
- Döring, L. (2014). A 0–1 law for spectrally positive Lévy processes conditioned to be positive.
