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

   in press

   arXiv Bib

   @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},
     note = {in press},
     year = {2024},
   }

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

   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

   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},
   }

2. 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},
   }