半线性慢速粗糙偏微分方程的平均原理

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-05-10 DOI:10.1016/j.spa.2025.104683

Miaomiao Li , Yunzhang Li , Bin Pei , Yong Xu

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引用次数: 0

摘要

研究了一类由有限维粗糙乘性噪声驱动的半线性慢速偏微分方程的平均原理。其中，慢分量由γ∈(1/3,1/2)的一般随机γ-Hölder粗路径驱动，而快分量由Itô-type布朗粗路径驱动。利用控制粗糙路径理论和经典的Khasminskii时间离散格式，证明了在Hölder拓扑下，慢分量强收敛于相应平均方程的解。

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Averaging principle for semilinear slow–fast rough partial differential equations

In this paper, we investigate the averaging principle for a class of semilinear slow–fast partial differential equations driven by finite-dimensional rough multiplicative noise. Specifically, the slow component is driven by a general random

γ

-Hölder rough path for some

γ \in (1 / 3, 1 / 2)

, while the fast component is driven by an Itô-type Brownian rough path. Using controlled rough path theory and the classical Khasminskii’s time discretization scheme, we demonstrate that the slow component converges strongly to the solution of the corresponding averaged equation under the Hölder topology.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.