6 citations · 18 across the 16 of their papers we have counts for
16 papers
Statistical Convergence of Spherical First Hitting Diffusion Models
Simon Bienewald, Lukas Trottner
Denoising diffusion models have evolved into a state-of-the-art method for tasks in various fields, such as denoising and generation of images, text generation, or generation of sy…
Reflected diffusion models adapt to low-dimensional data
Asbjørn Holk, Claudia Strauch, Lukas Trottner
While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data re…
In situ Learning-Based Spin Engineering of Pulsed Dynamic Nuclear Polarization
Filip V. Jensen, José P. Carvalho, Nino Wili +6
Pulsed Dynamic Nuclear Polarization (DNP) is currently receiving substantial interest as a means to enhance the sensitivity of nuclear magnetic resonance (NMR) and magnetic resonan…
Model-free filtering in high dimensions via projection and score-based diffusions
Sören Christensen, Jan Kallsen, Claudia Strauch +1
We consider the problem of recovering a latent signal from its noisy observation . The unknown law of , and in particular its support , are ac…
Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions
Sören Christensen, Jan Kallsen, Claudia Strauch +1
We introduce a new class of generative diffusion models that, unlike conventional denoising diffusion models, achieve a time-homogeneous structure for both the noising and denoisin…
Statistical guarantees for denoising reflected diffusion models
Asbjørn Holk, Claudia Strauch, Lukas Trottner
In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical…
Multivariate change estimation for a stochastic heat equation from local measurements
Anton Tiepner, Lukas Trottner
We study a stochastic heat equation with piecewise constant diffusivity having a jump at a hypersurface that splits the underlying space , into two disjo…
The uniqueness of the Wiener-Hopf factorisation of Lévy processes and random walks
Leif Döring, Mladen Savov, Lukas Trottner +1
We prove that the spatial Wiener-Hopf factorisation of a Lévy process or random walk without killing is unique.
Data-driven rules for multidimensional reflection problems
Sören Christensen, Asbjørn Holk Thomsen, Lukas Trottner
Over the recent past data-driven algorithms for solving stochastic optimal control problems in face of model uncertainty have become an increasingly active area of research. Howeve…
Markov additive friendships
Leif Döring, Lukas Trottner, Alexander R. Watson
The Wiener--Hopf factorisation of a Lévy or Markov additive process describes the way that it attains new maxima and minima in terms of a pair of so-called ladder height processes.…
Covariate shift in nonparametric regression with Markovian design
Lukas Trottner
Covariate shift in regression problems and the associated distribution mismatch between training and test data is a commonly encountered phenomenon in machine learning. In this pap…
Change point estimation for a stochastic heat equation
Markus Reiß, Claudia Strauch, Lukas Trottner
We study a change point model based on a stochastic partial differential equation (SPDE) corresponding to the heat equation governed by the weighted Laplacian $Δ_\vartheta = \nabla…
Concentration analysis of multivariate elliptic diffusion processes
Cathrine Aeckerle-Willems, Claudia Strauch, Lukas Trottner
We prove concentration inequalities and associated PAC bounds for continuous- and discrete-time additive functionals for possibly unbounded functions of multivariate, nonreversible…
Learning to reflect: A unifying approach for data-driven stochastic control strategies
Sören Christensen, Claudia Strauch, Lukas Trottner
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoret…
Stability of overshoots of Markov additive processes
Leif Döring, Lukas Trottner
We prove precise stability results for overshoots of Markov additive processes (MAPs) with finite modulating space. Our approach is based on the Markovian nature of overshoots of M…
Mixing it up: A general framework for Markovian statistics
Niklas Dexheimer, Claudia Strauch, Lukas Trottner
Up to now, the nonparametric analysis of multidimensional continuous-time Markov processes has focussed strongly on specific model choices, mostly related to symmetry of the semigr…