6 citations · 18 across the 16 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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…
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…
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…