6 citations · 24 across the 14 of their papers we have counts for
14 papers
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…
Nonparametric velocity estimation in stochastic convection-diffusion equations from multiple local measurements
Claudia Strauch, Anton Tiepner
We investigate pointwise estimation of the function-valued velocity field of a second-order linear SPDE. Based on multiple spatially localised measurements, we construct a weighted…
Data-driven optimal stopping: A pure exploration analysis
Sören Christensen, Niklas Dexheimer, Claudia Strauch
The standard theory of optimal stopping is based on the idealised assumption that the underlying process is essentially known. In this paper, we drop this restriction and study dat…
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…
On Lasso and Slope drift estimators for Lévy-driven Ornstein--Uhlenbeck processes
Niklas Dexheimer, Claudia Strauch
We investigate the problem of estimating the drift parameter of a high-dimensional Lévy-driven Ornstein--Uhlenbeck process under sparsity constraints. It is shown that both Lasso a…
Estimating the characteristics of stochastic damping Hamiltonian systems from continuous observations
Niklas Dexheimer, Claudia Strauch
We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Ham…
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…
Nonparametric learning for impulse control problems
Sören Christensen, Claudia Strauch
One of the fundamental assumptions in stochastic control of continuous time processes is that the dynamics of the underlying (diffusion) process is known. This is, however, usually…
Sup-norm adaptive simultaneous drift estimation for ergodic diffusions
Cathrine Aeckerle-Willems, Claudia Strauch
We consider the question of estimating the drift and the invariant density for a large class of scalar ergodic diffusion processes, based on continuous observations, in -norm…
Concentration of scalar ergodic diffusions and some statistical implications
Cathrine Aeckerle-Willems, Claudia Strauch
We derive uniform concentration inequalities for continuous-time analogues of empirical processes and related stochastic integrals of scalar ergodic diffusion processes. Thereby, w…
Uniform Central Limit Theorems for Multidimensional Diffusions
Angelika Rohde, Claudia Strauch
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empiri…