Zobrazeno 1 - 10
of 22
pro vyhledávání: '"Zimmer, Raphael"'
Autor:
Alt, Tobias, Ibisch, Andrea, Meiser, Clemens, Wilhelm, Anna, Zimmer, Raphael, Berghoff, Christian, Droste, Christoph, Karschau, Jens, Laus, Friederike, Plaga, Rainer, Plesch, Carola, Sennewald, Britta, Thaeren, Thomas, Unverricht, Kristina, Waurick, Steffen
Generative AI models are capable of performing a wide range of tasks that traditionally require creativity and human understanding. They learn patterns from existing data during training and can subsequently generate new content such as texts, images
Externí odkaz:
http://arxiv.org/abs/2406.04734
Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction potentials. The approach is based on a combination of reflection and s
Externí odkaz:
http://arxiv.org/abs/1805.11387
Publikováno v:
Ann. Appl. Probab., Volume 30, Number 3 (2020), 1209-1250
Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is explicit. Globa
Externí odkaz:
http://arxiv.org/abs/1805.00452
We introduce a new probabilistic approach to quantify convergence to equilibrium for (kinetic) Langevin processes. In contrast to previous analytic approaches that focus on the associated kinetic Fokker-Planck equation, our approach is based on a spe
Externí odkaz:
http://arxiv.org/abs/1703.01617
Autor:
Eberle, Andreas, Zimmer, Raphael
We present a novel approach of coupling two multidimensional and non-degenerate It\^o processes $(X_t)$ and $(Y_t)$ which follow dynamics with different drifts. Our coupling is sticky in the sense that there is a stochastic process $(r_t)$, which sol
Externí odkaz:
http://arxiv.org/abs/1612.06125
Publikováno v:
The Annals of Applied Probability, 2020 Jun 01. 30(3), 1209-1250.
Externí odkaz:
https://www.jstor.org/stable/26965973
We consider $\mathbb{R}^d$-valued diffusion processes of type \begin{align*} dX_t\ =\ b(X_t)dt\, +\, dB_t. \end{align*} Assuming a geometric drift condition, we establish contractions of the transitions kernels in Kantorovich ($L^1$ Wasserstein) dist
Externí odkaz:
http://arxiv.org/abs/1606.06012
Autor:
Zimmer, Raphael
Given a separable and real Hilbert space $\mathbb{H}$ and a trace-class, symmetric and non-negative operator $\mathcal{G}:\mathbb{H}\rightarrow\mathbb{H}$, we examine the equation \begin{align*} dX_t = -X_t\, dt + b(X_t) \, dt + \sqrt{2} \, dW_t, \qq
Externí odkaz:
http://arxiv.org/abs/1605.07863
Publikováno v:
The Annals of Probability, 2019 Jul 01. 47(4), 1982-2010.
Externí odkaz:
https://www.jstor.org/stable/26754241
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