迪安-川崎方程的非线性 SPDE 近似的弱误差分析

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-03-15 DOI:10.1007/s40072-024-00324-1

Ana Djurdjevac, Helena Kremp, Nicolas Perkowski

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引用次数: 0

摘要

我们考虑对独立粒子的迪安-川崎方程进行非线性 SPDE 近似。我们的近似方法满足粒子系统的物理约束，即其解在所有时间内都是一个概率量（保持正向性和质量守恒）。利用对偶论证，我们证明粒子系统与非线性 SPDE 之间的弱误差为 \(N^{-1-1/(d/2+1)}\log N\) 量级。同时，我们还展示了一类具有 Itô 噪声的非线性正则化 Dean-Kawasaki 方程的拟合性、比较原理和熵估计。

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Weak error analysis for a nonlinear SPDE approximation of the Dean–Kawasaki equation

We consider a nonlinear SPDE approximation of the Dean–Kawasaki equation for independent particles. Our approximation satisfies the physical constraints of the particle system, i.e. its solution is a probability measure for all times (preservation of positivity and mass conservation). Using a duality argument, we prove that the weak error between particle system and nonlinear SPDE is of the order \(N^{-1-1/(d/2+1)}\log N\). Along the way we show well-posedness, a comparison principle, and an entropy estimate for a class of nonlinear regularized Dean–Kawasaki equations with Itô noise.

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来源期刊

Stochastics and Partial Differential Equations-Analysis and Computations Mathematics-Modeling and Simulation

CiteScore

2.70

自引率

13.30%

发文量

期刊介绍： Stochastics and Partial Differential Equations: Analysis and Computations publishes the highest quality articles presenting significantly new and important developments in the SPDE theory and applications. SPDE is an active interdisciplinary area at the crossroads of stochastic anaylsis, partial differential equations and scientific computing. Statistical physics, fluid dynamics, financial modeling, nonlinear filtering, super-processes, continuum physics and, recently, uncertainty quantification are important contributors to and major users of the theory and practice of SPDEs. The journal is promoting synergetic activities between the SPDE theory, applications, and related large scale computations. The journal also welcomes high quality articles in fields strongly connected to SPDE such as stochastic differential equations in infinite-dimensional state spaces or probabilistic approaches to solving deterministic PDEs.