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pro vyhledávání: '"65C30"'
We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formulate a non-iterative domain decomposition approach. Such methods can hel
Externí odkaz:
http://arxiv.org/abs/2412.10125
Autor:
Wang, Binxu, Vastola, John J.
Publikováno v:
Transactions on Machine Learning Research, 2024. https://openreview.net/forum?id=I0uknSHM2j
By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates to the scor
Externí odkaz:
http://arxiv.org/abs/2412.09726
In recent years, stochastic effects have become increasingly relevant for describing fluid behaviour, particularly in the context of turbulence. The most important model for inviscid fluids in computational fluid dynamics are the Euler equations of g
Externí odkaz:
http://arxiv.org/abs/2412.07613
We consider the numerical approximation of the stochastic complex Ginzburg-Landau equation with additive noise on the one dimensional torus. The complex nature of the equation means that many of the standard approaches developed for stochastic partia
Externí odkaz:
http://arxiv.org/abs/2412.07206
Autor:
Schuh, Katharina, Souttar, Iain
We establish general conditions under which there exists uniform in time convergence between a stochastic process and its approximated system. These standardised conditions consist of a local in time estimate between the original and the approximated
Externí odkaz:
http://arxiv.org/abs/2412.05239
Strong convergence of the Euler scheme for singular kinetic SDEs driven by $\alpha$-stable processes
Autor:
Ling, Chengcheng
We study the strong approximation of the solutions to singular stochastic kinetic equations (also referred to as second-order SDEs) driven by $\alpha$-stable processes, using an Euler-type scheme inspired by [11]. For these equations, the stability i
Externí odkaz:
http://arxiv.org/abs/2412.05142
This paper investigates the pathwise uniform convergence in probability of fully discrete finite-element approximations for the two-dimensional stochastic Navier-Stokes equations with multiplicative noise, subject to no-slip boundary conditions. Assu
Externí odkaz:
http://arxiv.org/abs/2412.04231
Autor:
Pang, Peter H. C.
In this note we construct solutions to rough differential equations ${\rm d} Y = f(Y) \,{\rm d} X$ with a driver $X \in C^\alpha([0,T];\mathbb{R}^d)$, $\frac13 < \alpha \le \frac12$, using a splitting-up scheme. We show convergence of our scheme to s
Externí odkaz:
http://arxiv.org/abs/2412.00432
Autor:
Jabbari, Rofeide, Olivares, Pablo
In this paper we extend models for the dynamic of the temperatures by considering random switching between Levy noises instead of Brownian motions, with a mean-reverting movement towards a seasonal periodic function. The use of Levy noises allows for
Externí odkaz:
http://arxiv.org/abs/2411.19192
Autor:
Giles, Michael B.
It is well known that the Euler-Maruyama discretisation of an autonomous SDE using a uniform timestep $h$ has a strong convergence error which is $O(h^{1/2})$ when the drift and diffusion are both globally Lipschitz. This note proves that the same is
Externí odkaz:
http://arxiv.org/abs/2411.15930