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. und Slowik, M. (2026). Gradient estimates of the heat kernel for random walks among time-dependent random conductances. Probability Theory and Related Fields, 1–50.
- Koß, M., Weissmann, S. und 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. und van Leeuven, T. (2026). Derivative-free stochastic bilevel optimization for inverse problems. Computational Optimization and Applications, 93, 967-1020.
- Sprungk, B., Weissmann, S. und Zech, J. (2025). Metropolis-adjusted interacting particle sampling. Statistics and Computing : SC, 35, 1–31.
- Baguley, S. P., Döring, L. und 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. und 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. und Watson, A. R. (2024). Markov additive friendships. Transactions of the American Mathematical Society, 377, 7699-7752.
- Weissmann, S., Klein, S., Azizian, W. und Döring, L. (2024). Almost sure convergence of stochastic gradient methods under gradient domination. Transactions on Machine Learning Research : TMLR, 2024, 1–40.
- Döring, L. und 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. und 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. und 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. und Weissmann, P. (2020). Stable processes conditioned to avoid an interval. Stochastic Processes and Their Applications, 130, 471–487.
- Döring, L. und 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. und Reichmann, O. (2019). On Skorokhod embeddings and Poisson equations. The Annals of Applied Probability, 29, 2302-2337.
- Döring, L., Watson, A. R. und 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. und Kyprianou, A. E. (2017). Real self-similar processes started from the origin. The Annals of Probability, 45, 1952-2003.
- Döring, L., Horvath, B. und 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. und 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. und Schmidt, M. U. (2017). Individualisierte Tutorien im Mathematikstudium. Neues Handbuch Hochschullehre, 82, 77–88.
- Döring, L. und Kyprianou, A. E. (2016). Perpetual integrals for Lévy processes. Journal of Theoretical Probability, 29, 1192-1198.
- Berestycki, J., Döring, L., Mytnik, L. und 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. und 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. und 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. und 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. und 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. und Döring, L. (2013). On entire moments of self-similar Markov processes. Stochastic Analysis and Applications, 31, 191–198.
- Barczy, M., Döring, L., Li, Z. und Pap, G. (2013). On parameter estimation for critical affine processes. Electronic Journal of Statistics : EJS, 7, 647–696.
- Döring, L. und Barczy, M. (2012). A jump-type SDE approach to positive self-similar Markov processes. Electronic Journal of Probability : EJP, 17, 1–39.
- Döring, L. und 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. und 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. und Etheridge, A. (2011). On the moments and the interface of the symbiotic branching model. The Annals of Probability, 39, 252–290.
- Döring, L. und Svavov, M. (2011). (Non)differentiability and asymptotics for potential densities of subordinators. Electronic Journal of Probability : EJP, 16, 470–503.
- Döring, L. und 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. und Reichmann, O. (2018). Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker-Planck equations. Mannheim [u. a.].
- Döring, L. und Kyprianou, A. E. (2018). Entrance and exit at infinity for stable jump diffusions. Mannheim [u. a.].
- Döring, L., Kyprianou, A. E. und Weissmann, P. (2018). Stable processes conditioned to avoid an interval. Mannheim [u. a.].
- Döring, L., Watson, A. R. und Weissmann, P. (2018). Lévy processes with finite variance conditioned to avoid an interval. Mannheim [u. a.].
- Döring, L. und Weissmann, P. (2018). Stable processes conditioned to hit an interval continuously from the outside. Mannheim [u. a.].
- Döring, L., Gonon, L., Prömel, D. J. und Reichmann, O. (2017). On Skorokhod embeddings and Poisson equations. Mannheim [u. a.].
- Dreieich, S. und Döring, L. (2014). Random interlacements via Kuznetsov measures. Mannheim [u. a.].
- Benning, F. und 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. und 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. und 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. und 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.
