Research
The research of our group focuses on mathematical topics within recent AI breakthroughs
- reinforcement learning, from theoretical convergence analysis to the design of new algorithms,
- optimisation methods such as stochastic gradient descent variants and their use in ML and AI,
- classical probability theory, stochastic process theory and applications in biology, medicine, statistical physics.
We used to publish our work in mathematics journals but now mostly submit to computer science conferences such as (NeurIPS, ICML, ICLR) and computer science journals like JMLR/
Publications
- Deuschel, J.-D., Kumagai, T. and Slowik, M. (2026). Gradient estimates of the heat kernel for random walks among time-dependent random conductances. Probability Theory and Related Fields, 195, 871–920.
- Koß, M., Weissmann, S. and Zech, J. (2026). On the mean-field limit of consensus-based methods. Mathematical Methods in the Applied Sciences : MMAS, 49, 4214-4240.
- Staudigl, M., Weissmann, S. and van Leeuven, T. (2026). Derivative-free stochastic bilevel optimization for inverse problems. Computational Optimization and Applications, 93, 967-1020.
- Sprungk, B., Weissmann, S. and Zech, J. (2025). Metropolis-adjusted interacting particle sampling. Statistics and Computing : SC, 35, 1–31.
- Baguley, S. P., Döring, L. and Kyprianou, A. E. (2024). General path integrals and stable SDEs. Journal of the European Mathematical Society : JEMS, 26, 3243-3286.
- 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, 56, 2951-2968.
- Döring, L., Trottner, L. and Watson, A. R. (2024). Markov additive friendships. Transactions of the American Mathematical Society, 377, 7699-7752.
- Weissmann, S., Klein, S., Azizian, W. and Döring, L. (2024). Almost sure convergence of stochastic gradient methods under gradient domination. Transactions on Machine Learning Research : TMLR, 2024, 1–40.
- Döring, L. and Trottner, L. (2023). Stability of overshoots of Markov additive processes. The Annals of Applied Probability, 33, 5413-5458.
- 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.
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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.].
- Benning, F. and Döring, L. (2025). Random function descent. In , Advances in Neural Information Processing Systems 37 (NeurIPS 2024) (S. 111248-111298). , Neural Information Processing Systems Foundation, Inc. (NeurIPS): .
- Klein, S., Weissmann, S. and Döring, L. (2024). Beyond stationarity: Convergence analysis of stochastic softmax policy gradient methods. In , The Twelfth International Conference on Learning Representations : ICLR 2024, Vienna, Austria, May 07 2024 (S. 1–54). , OpenReview.net: .
- 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.
