粗糙演化方程的不稳定流形

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Stochastics and Dynamics Pub Date : 2023-02-03 DOI:10.1142/s0219493722400330

Hongyan Ma, Hongjun Gao

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引用次数: 0

摘要

本文考虑一类由无限维γ-Hölder粗糙路径驱动的粗糙非线性演化方程，其γ∈(1/3,1/2)。首先，利用粗糙路径理论给出了无限维γ-Hölder粗糙路径的固有积分。其次，我们得到了粗糙演化方程的全局时间解和随机动力系统。最后，利用适当离散的Lyapunov-Perron方法，导出了粗糙演化方程局部不稳定流形的存在性。

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Unstable manifolds for rough evolution equations

In this paper, we consider a class of rough nonlinear evolution equations driven by infinite-dimensional $γ$ -Hölder rough paths with $γ \in (1 / 3, 1 / 2]$ . First, we give a proper integral with respect to infinite-dimensional $γ$ -Hölder rough paths by using rough paths theory. Second, we obtain the global in time solution and random dynamical system of rough evolution equation. Finally, we derive the existence of local unstable manifolds for rough evolution equations by a properly discretized Lyapunov–Perron method.

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来源期刊

Stochastics and Dynamics 数学-统计学与概率论

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal is devoted to publishing high quality papers in modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system''s point of view. Papers can be about theory, experiments, algorithms, numerical simulation and applications. Papers studying the dynamics of stochastic phenomena by means of random or stochastic ordinary, partial or functional differential equations or random mappings are particularly welcome, and so are studies of stochasticity in deterministic systems.