具有记忆的随机动力系统的密度演化:一个通用算法。

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2025-05-01 DOI:10.1063/5.0258144
Xianming Liu, Thomas Sun
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引用次数: 0

摘要

具有记忆的随机动力系统通常用随机泛函微分方程来建模。量化这些系统的概率密度演化仍然是一个具有很强实际应用价值的开放性问题。然而,由于缺乏计算随机泛函微分方程一般形式的概率密度的有效方法,这些系统的应用受到严重限制。我们通过提出一种通用的方法来计算一类具有记忆的随机动力系统的概率密度演变来解决这一挑战。该方法通过从欧拉格式导出的离散模型逼近随机泛函方程,并通过计算离散对应的概率密度递归地估计其概率密度。该方法具有确定性和计算效率。为了验证和证明其有效性,我们将其应用于计算一些典型气候模式的瞬态和长期概率密度演变。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Density evolution in stochastic dynamical systems with memory: A universal algorithm.

Stochastic dynamical systems with memory are usually modeled using stochastic functional differential equations. Quantifying the probability density evolution in these systems remains an open problem with strong practical applications. However, due to a lack of efficient methods for computing the probability density of stochastic functional differential equations in their general form, the application of these systems are severely restricted. We address this challenge by presenting a universal approach for computing the evolution of probability density in a broad class of stochastic dynamical systems with memory. The proposed approach approximates the stochastic functional equation via a discrete model derived from the Euler scheme and recursively estimates its probability density by computing that of the discretized counterpart. The method is deterministic and computationally efficient. To validate and demonstrate its effectiveness, we apply it to compute both transient and long-term probability density evolution for some typical climate models.

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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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