publications

journal articles

1. JUQ

   Data-driven rules for multidimensional reflection problems

   Sören Christensen, Asbjørn Holk Thomsen, and Lukas Trottner

   SIAM/ASA J. Uncertain. Quantif., 2024

   arXiv Bib HTML

   @article{christensen23,
     author = {Christensen, S{\"o}ren and Thomsen, Asbj{\o}rn Holk and Trottner, Lukas},
     journal = {SIAM/ASA J. Uncertain. Quantif.},
     title = {Data-driven rules for multidimensional reflection problems},
     year = {2024},
     volume = {12},
     number = {4},
     pages = {1240-1272},
   }

2. TAMS

   Markov additive friendships

   Leif Döring, Lukas Trottner, and Alexander R. Watson

   Trans. Amer. Math. Soc., 2024

   arXiv Bib HTML

   @article{doering23b,
     author = {D{\"o}ring, Leif and Trottner, Lukas and Watson, Alexander R.},
     journal = {Trans. Amer. Math. Soc.},
     title = {Markov additive friendships},
     volume = {377},
     number = {11},
     year = {2024},
   }

3. BLMS

   The uniqueness of the Wiener–Hopf factorisation of Lévy processes and random walks

   Leif Döring, Mladen Savov, Lukas Trottner, and Alexander R. Watson

   Bull. Lond. Math. Soc., 2024

   arXiv Bib HTML

   @article{doering23c,
     author = {D{\"o}ring, Leif and Savov, Mladen and Trottner, Lukas and Watson, Alexander R.},
     journal = {Bull. Lond. Math. Soc.},
     title = {The uniqueness of the Wiener--Hopf factorisation of L{\'e}vy processes and random walks},
     volume = {56},
     number = {9},
     pages = {2951–2968},
     year = {2024},
   }

4. IMAIAI

   Covariate shift in nonparametric regression with Markovian design

   Lukas Trottner

   Inf. Inference, 2024

   arXiv Bib HTML

   @article{trottner24,
     author = {Trottner, Lukas},
     fjournal = {Information and Inference. A Journal of the IMA},
     issn = {2049-8764,2049-8772},
     journal = {Inf. Inference},
     number = {2},
     pages = {Paper No. iaae011},
     title = {Covariate shift in nonparametric regression with {M}arkovian design},
     volume = {13},
     year = {2024},
   }

5. Bernoulli

   Learning to reflect: A unifying approach for data-driven stochastic control strategies

   Sören Christensen, Claudia Strauch, and Lukas Trottner

   Bernoulli, 2024

   Bib HTML

   @article{chr24,
     author = {Christensen, S\"{o}ren and Strauch, Claudia and Trottner, Lukas},
     fjournal = {Bernoulli},
     journal = {Bernoulli},
     number = {3},
     pages = {2074--2101},
     title = {Learning to reflect: {A} unifying approach for data-driven stochastic control strategies},
     url = {https://doi.org/10.3150/23-bej1665},
     volume = {30},
     year = {2024},
   }

6. AOAP

   Stability of overshoots of Markov additive processes

   Leif Döring, and Lukas Trottner

   Ann. Appl. Probab., 2023

   arXiv Bib HTML

   @article{doering23,
     author = {D\"{o}ring, Leif and Trottner, Lukas},
     fjournal = {The Annals of Applied Probability},
     issn = {1050-5164,2168-8737},
     journal = {Ann. Appl. Probab.},
     mrclass = {60J25 (37A25 62M05)},
     mrnumber = {4677737},
     number = {6B},
     pages = {5413--5458},
     title = {Stability of overshoots of {M}arkov additive processes},
     volume = {33},
     year = {2023},
   }

7. JMLR

   Concentration analysis of multivariate elliptic diffusions

   Lukas Trottner, Cathrine Aeckerle-Willems, and Claudia Strauch

   J. Mach. Learn. Res., 2023

   Bib HTML

   @article{trottner23,
     author = {Trottner, Lukas and Aeckerle-Willems, Cathrine and Strauch, Claudia},
     issn = {1532-4435},
     journal = {J. Mach. Learn. Res.},
     pages = {Paper No. 106, pp. 1--38},
     title = {Concentration analysis of multivariate elliptic diffusions},
     volume = {24},
     year = {2023},
   }

8. AIHP

   Adaptive invariant density estimation for continuous-time mixing Markov processes under sup-norm risk

   Niklas Dexheimer, Claudia Strauch, and Lukas Trottner

   Ann. Inst. Henri Poincaré Probab. Stat., 2022

   Bib HTML

   @article{dexheimer22,
     author = {Dexheimer, Niklas and Strauch, Claudia and Trottner, Lukas},
     fjournal = {Annales de l'Institut Henri Poincar\'{e} Probabilit\'{e}s et Statistiques},
     issn = {0246-0203},
     journal = {Ann. Inst. Henri Poincar\'{e} Probab. Stat.},
     mrclass = {62M05 (60G10 60J25 62G05 62G20)},
     number = {4},
     pages = {2029--2064},
     title = {Adaptive invariant density estimation for continuous-time mixing {M}arkov processes under sup-norm risk},
     url = {https://doi.org/10.1214/21-aihp1235},
     volume = {58},
     year = {2022},
   }

preprints

1. arXiv

   Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions

   Sören Christensen, Claudia Strauch, and Lukas Trottner

   2025

   arXiv Bib

   @misc{cst24,
     title = {Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions},
     author = {Christensen, Sören and Strauch, Claudia and Trottner, Lukas},
     year = {2025},
     eprint = {2501.19373},
     archiveprefix = {arXiv},
     primaryclass = {stat.ML},
   }

2. arXiv

   Statistical guarantees for denoising reflected diffusion models

   Asbjørn Holk, Claudia Strauch, and Lukas Trottner

   2024

   arXiv Bib

   @misc{hst24,
     title = {Statistical guarantees for denoising reflected diffusion models},
     author = {Holk, Asbjørn and Strauch, Claudia and Trottner, Lukas},
     year = {2024},
     eprint = {2411.01563},
     archiveprefix = {arXiv},
     primaryclass = {math.ST},
   }

3. arXiv

   Multivariate change estimation for a stochastic heat equation from local measurements

   Anton Tiepner, and Lukas Trottner

   2024

   arXiv Bib

   @misc{tt24,
     archiveprefix = {arXiv},
     author = {Tiepner, Anton and Trottner, Lukas},
     eprint = {2409.15059},
     primaryclass = {math.ST},
     title = {Multivariate change estimation for a stochastic heat equation from local measurements},
     year = {2024},
   }

4. arXiv

   Change point estimation for a stochastic heat equation

   Markus Reiß, Claudia Strauch, and Lukas Trottner

   2023

   arXiv Bib

   @misc{reiss23,
     archiveprefix = {arXiv},
     author = {Rei{\ss}, Markus and Strauch, Claudia and Trottner, Lukas},
     eprint = {2307.10960},
     primaryclass = {math.ST},
     title = {Change point estimation for a stochastic heat equation},
     year = {2023},
   }