Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Trottner, Lukas"'
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 advances have delivered explanations for the generation ability of ide
Externí odkaz:
http://arxiv.org/abs/2411.01563
Autor:
Tiepner, Anton, Trottner, Lukas
We study a stochastic heat equation with piecewise constant diffusivity $\theta$ having a jump at a hypersurface $\Gamma$ that splits the underlying space $[0,1]^d$, $d\geq2,$ into two disjoint sets $\Lambda_-\cup\Lambda_+.$ Based on multiple spatial
Externí odkaz:
http://arxiv.org/abs/2409.15059
We prove that the spatial Wiener-Hopf factorisation of a L\'evy process or random walk without killing is unique.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2312.13106
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. However, for singular controls and underlying diffusion dynamics the analysi
Externí odkaz:
http://arxiv.org/abs/2311.06639
The Wiener--Hopf factorisation of a L\'evy 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. Vigon's theory of friendship for L\'evy processes addresses the inv
Externí odkaz:
http://arxiv.org/abs/2308.09432
We study a change point model based on a stochastic partial differential equation (SPDE) corresponding to the heat equation governed by the weighted Laplacian $\Delta_\vartheta = \nabla\vartheta\nabla$, where $\vartheta=\vartheta(x)$ is a space-depen
Externí odkaz:
http://arxiv.org/abs/2307.10960
Autor:
Trottner, Lukas
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 paper, we extend recent results on nonparametric convergence rates for i.
Externí odkaz:
http://arxiv.org/abs/2307.08517
Publikováno v:
Journal of Machine Learning Research 24 (2023), paper no. 106, pp. 1-38
We prove concentration inequalities and associated PAC bounds for continuous- and discrete-time additive functionals for possibly unbounded functions of multivariate, nonreversible diffusion processes. Our analysis relies on an approach via the Poiss
Externí odkaz:
http://arxiv.org/abs/2206.03329
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 theoretical solutions are well understood in many scenarios, their practicabi
Externí odkaz:
http://arxiv.org/abs/2104.11496
Autor:
Döring, Leif, Trottner, Lukas
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 MAPs whose mixing and ergodic properties are investigated in terms of t
Externí odkaz:
http://arxiv.org/abs/2102.03238