Evolution of moments of isotropic Brownian stochastic flows
V. V. Fomichov
TL;DR
This paper investigates the long-term behavior of all moments related to distances between particles in an isotropic Brownian stochastic flow, which approximates the Arratia flow, providing insights into its asymptotic properties.
Contribution
It offers a comprehensive analysis of the asymptotic moments of the flow, extending understanding of stochastic flow behavior and its approximation to the Arratia flow.
Findings
Derived asymptotic formulas for all moments of interparticle distances.
Established the behavior of mixed moments in the flow.
Provided a smooth approximation framework for the Arratia flow.
Abstract
In this paper we consider the asymptotic behaviour of all moments of the interparticle distance and of all mixed moments of an isotropic Brownian stochastic flow which serves as a smooth approximation of the Arratia flow.
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Taxonomy
TopicsStochastic processes and financial applications · Mathematical Dynamics and Fractals · Stochastic processes and statistical mechanics