Zobrazeno 1 - 10
of 1 016
pro vyhledávání: '"Stein, Andreas"'
Autor:
Haji-Al, Abdul-Lateef, Stein, Andreas
We present a novel multilevel Monte Carlo approach for estimating quantities of interest for stochastic partial differential equations (SPDEs). Drawing inspiration from [Giles and Szpruch: Antithetic multilevel Monte Carlo estimation for multi-dimens
Externí odkaz:
http://arxiv.org/abs/2307.14169
We establish universality and expression rate bounds for a class of neural Deep Operator Networks (DON) emulating Lipschitz (or H\"older) continuous maps $\mathcal G:\mathcal X\to\mathcal Y$ between (subsets of) separable Hilbert spaces $\mathcal X$,
Externí odkaz:
http://arxiv.org/abs/2307.09835
We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and V\"ollering, 2016] and prove a strong law of
Externí odkaz:
http://arxiv.org/abs/2303.06756
Autor:
Stein, Andreas, Hoang, Viet Ha
We propose a multilevel Monte Carlo-FEM algorithm to solve elliptic Bayesian inverse problems with "Besov random tree prior". These priors are given by a wavelet series with stochastic coefficients, and certain terms in the expansion vanishing at ran
Externí odkaz:
http://arxiv.org/abs/2302.00678
Autor:
Schwab, Christoph, Stein, Andreas
We develop a multilevel Monte Carlo (MLMC)-FEM algorithm for linear, elliptic diffusion problems in polytopal domain $\mathcal D\subset \mathbb R^d$, with Besov-tree random coefficients. This is to say that the logarithms of the diffusion coefficient
Externí odkaz:
http://arxiv.org/abs/2302.00522
We propose a novel a-posteriori error estimation technique where the target quantities of interest are ratios of high-dimensional integrals, as occur e.g. in PDE constrained Bayesian inversion and PDE constrained optimal control subject to an entropi
Externí odkaz:
http://arxiv.org/abs/2301.03327
We consider a directed random walk on the backbone of the supercritical oriented percolation cluster in dimensions $d+1$ with $d \ge 3$ being the spatial dimension. For this random walk we prove an annealed local central limit theorem and a quenched
Externí odkaz:
http://arxiv.org/abs/2105.09030
We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb Z$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations decrease ac
Externí odkaz:
http://arxiv.org/abs/2009.10927
We construct graphs (trees of bounded degree) on which the contact process has critical rate (which will be the same for both global and local survival) equal to any prescribed value between zero and $\lambda_c(\mathbb{Z})$, the critical rate of the
Externí odkaz:
http://arxiv.org/abs/2005.00420