A Unifying Theory of Massive Particle Systems, Wasserstein Brownian Motions, and the Dean–Kawasaki Equation
This paper establishes a unifying theory connecting infinite systems of interacting massive particles, solutions to the Dean–Kawasaki equation, Wasserstein diffusions, and metric measure Brownian motions, demonstrating their equivalence and exploring their properties in depth.
Dean-Kawasaki 模型在 Vlasov-Fokker-Planck 類型方程式中的適定性：僅適用於原子初始數據
對於描述相互作用粒子系統的 Dean-Kawasaki 模型，其解僅在初始數據為原子數據時存在，而對於平滑初始數據則不存在解，這突顯了此類模型對初始數據的敏感性。
Vlasov-Fokker-Planck 유형의 Dean-Kawasaki 모델에 대한 Well-Posedness: 원자 초기 데이터에 대한 해의 존재성 및 매끄러운 초기 데이터에 대한 해의 부재 증명
이 논문은 입자 시스템의 집단적 진화를 설명하는 확률론적 편미분 방정식(SPDE)인 Vlasov-Fokker-Planck 유형 Dean-Kawasaki 모델의 해의 존재성과 유일성에 대한 조건을 제시합니다. 특히, 특정 원자 측정을 제외하고 매끄러운 초기 데이터에 대한 해가 존재하지 않음을 보여줍니다.
Well-Posedness of Dean-Kawasaki Models for Interacting Particle Systems with Inertia: Existence and Uniqueness of Solutions for Atomic Initial Data
This article investigates a class of stochastic partial differential equations (SPDEs) modeling interacting particle systems with inertia, proving that solutions exist only for a specific type of initial data representing discrete particles, highlighting the equations' sensitivity to initial conditions.
Polynomial Mixing Rate of the Stochastically Forced Kuramoto-Sivashinsky Equation on the Real Line
This research paper proves the existence of a unique stationary measure for the white-forced Kuramoto-Sivashinsky equation on the whole real line, demonstrating its convergence at a polynomial rate under specific conditions.
Moment Estimates for the Stochastic Heat Equation: Exploring the Impact of Curvature on Cartan-Hadamard Manifolds
This paper investigates the effect of negative curvature on the behavior of the stochastic heat equation, demonstrating that the growth rate of the solution's moments is influenced by the manifold's curvature and the noise regularity.
論局部李普希兹係數隨機偏微分方程的適定性
This research paper establishes the well-posedness (existence, uniqueness, and stability of solutions) of a stochastic partial differential equation (SPDE) with locally Lipschitz coefficients and linear growth conditions, extending classical results for SDEs to the infinite-dimensional setting.
Time-Dependent Spatial Averages of a Critical Stochastic Heat Equation in Dimensions Three and Higher
The time-dependent spatial averages of a critical stochastic heat equation exhibit different limiting behaviors depending on the relationship between time and spatial scales: a central limit theorem holds when time is much smaller than the squared radius, a non-Gaussian limit emerges when time is comparable to the squared radius, and extinction occurs when time significantly exceeds the squared radius.
具有乘法雜訊的拋物線隨機偏微分方程的高頻分析（部分結果）
本文針對一類由乘法高斯雜訊驅動的拋物線隨機偏微分方程（SPDE），探討其解的冪變異數和其他相關泛函的中心極限定理。研究發現，當雜訊的空間相關函數由階數 α ∈ (0, 1) 的里斯核給出時，儘管乘法雜訊係數的正則性較低，但中心極限定理中並不存在漸近偏差。
곱셈 잡음이 있는 포물선형 확률 편미분 방정식의 고주파 분석 - 비편향 중심 극한 정리 증명
곱셈 잡음이 있는 포물선형 확률 편미분 방정식(SPDE)의 해에 대한 정규화된 거듭제곱 변동에 대한 중심 극한 정리를 증명하고, 잡음 계수의 낮은 정규성에도 불구하고 점근적 편향이 없음을 보여줍니다.
© 2024 by Linnk AI