Most Probable Flows for Kunita SDEs

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-02-28 DOI:10.1007/s00245-024-10110-z

Erlend Grong, Stefan Sommer

引用次数: 0

Abstract

We identify most probable flows for Kunita Brownian motions, i.e. stochastic flows with Eulerian noise and deterministic drifts. Such stochastic processes appear for example in fluid dynamics and shape analysis modelling coarse scale deterministic dynamics together with fine-grained noise. We treat this infinite dimensional problem by equipping the underlying domain with a Riemannian metric originating from the noise. The resulting most probable flows are compared with the non-perturbed deterministic flow, both analytically and experimentally by integrating the equations with various choice of noise structures.

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库尼塔 SDE 的最可能流量

我们确定了库尼塔布朗运动的最可能流，即带有欧拉噪声和确定性漂移的随机流。例如，这种随机过程出现在流体动力学和形状分析中，以粗尺度确定性动力学和细粒度噪声为模型。我们在处理这个无限维问题时，在底层域中加入了源自噪声的黎曼度量。通过分析和实验，我们将所得到的最有可能的流动与未受扰动的确定性流动进行了比较，并对方程进行了积分，同时选择了不同的噪声结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.