Stochastic Lagrangian flows on the group of volume-preserving homeomorphisms of the spheres

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2013-12-09 DOI:10.1080/17442508.2014.995659

Dejun Luo

引用次数: 4

Abstract

We consider stochastic differential equations on the group of volume-preserving homeomorphisms of the sphere . The diffusion part is given by the divergence-free eigenvector fields of the Laplacian acting on -vector fields, while the drift is some other divergence-free vector field. We show that the equation generates a unique flow of measure-preserving homeomorphisms when the drift has first-order Sobolev regularity, and derive a formula for the distance between two Lagrangian flows. We also compute the rotation process of two particles on the sphere when they are close to each other.

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球的保容同胚群上的随机拉格朗日流

研究了球的保体积同胚群上的随机微分方程。扩散部分由作用于-向量场的拉普拉斯函数的无散度特征向量场给出，而漂移部分则是另一个无散度的向量场。我们证明了当漂移具有一阶Sobolev正则性时，该方程产生了唯一的保测度同胚流，并导出了两个拉格朗日流之间距离的公式。我们还计算了两个粒子在球上相互靠近时的旋转过程。

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

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.