Zobrazeno 1 - 10
of 95
pro vyhledávání: '"Avelin, Benny"'
Autor:
Avelin, Benny, Kuusi, Tuomo, Nummi, Patrik, Saksman, Eero, Tölle, Jonas M., Viitasaari, Lauri
We study periodic solutions to the following divergence-form stochastic partial differential equation with Wick-renormalized gradient on the $d$-dimensional flat torus $\mathbb{T}^d$, \[ -\nabla\cdot\left(e^{\diamond (- \beta X) }\diamond\nabla U\rig
Externí odkaz:
http://arxiv.org/abs/2405.17195
Autor:
Avelin, Benny, Hou, Mingyi
In this paper, we investigate weak solutions and Perron-Wiener-Brelot solutions to the linear kinetic Fokker-Planck equation in bounded domains. We establish the existence of weak solutions by applying the Lions-Lax-Milgram theorem and the vanishing
Externí odkaz:
http://arxiv.org/abs/2405.04070
Autor:
Avelin, Benny, Kuusi, Tuomo, Nummi, Patrik, Saksman, Eero, Tölle, Jonas M., Viitasaari, Lauri
We study unique solvability for one dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove well-posedness for Dirichlet, Neumann and periodic boundary data, and th
Externí odkaz:
http://arxiv.org/abs/2402.09127
Autor:
Avelin, Benny
In this paper we explore the concept of sequential inductive prediction intervals using theory from sequential testing. We furthermore introduce a 3-parameter PAC definition of prediction intervals that allows us via simulation to achieve almost shar
Externí odkaz:
http://arxiv.org/abs/2312.04950
We study the effect of approximation errors in assessing the extreme behavior of heavy-tailed random objects. We give conditions for the approximation error such that the standard asymptotic results hold for the classical Hill estimator and the corre
Externí odkaz:
http://arxiv.org/abs/2307.03581
Publikováno v:
Kinetic and Related Models, 2024, 17(4): 634-658
In this paper, we develop a Galerkin-type approximation, with quantitative error estimates, for weak solutions to the Cauchy problem for kinetic Fokker-Planck equations in the domain $(0, T) \times D \times \mathbb{R}^d$, where $D$ is either $\mathbb
Externí odkaz:
http://arxiv.org/abs/2305.14234
Autor:
Andersson, Martin, Avelin, Benny
We develop theory and methods that use the graph Laplacian to analyze the geometry of the underlying manifold of datasets. Our theory provides theoretical guarantees and explicit bounds on the functional forms of the graph Laplacian when it acts on f
Externí odkaz:
http://arxiv.org/abs/2301.00201
Autor:
Avelin, Benny, Viitasaari, Lauri
In this article we prove that estimator stability is enough to show that leave-one-out cross validation is a sound procedure, by providing concentration bounds in a general framework. In particular, we provide concentration bounds beyond Lipschitz co
Externí odkaz:
http://arxiv.org/abs/2211.02478
Autor:
Avelin, Benny, Julin, Vesa
In this paper we further develop the ideas from Geometric Function Theory initially introduced in [arXiv:2206.13206], to derive capacity estimate in metastability for arbitrary configurations. The novelty of this paper is twofold. First, the graph th
Externí odkaz:
http://arxiv.org/abs/2210.08787
In this paper we consider the mean transition time of an over-damped Brownian particle between local minima of a smooth potential. When the minima and saddles are non-degenerate this is in the low noise regime exactly characterized by the so called E
Externí odkaz:
http://arxiv.org/abs/2206.13206