Foliated stochastic calculus: Harmonic measures
Pedro J. Catuogno, Diego S. Ledesma, Paulo R. Ruffino
TL;DR
This paper develops a stochastic calculus framework for foliated manifolds, enabling analysis of harmonic measures and decomposing Laplacians, with applications to invariant measures and density equations.
Contribution
It introduces an intrinsic stochastic calculus for foliations and provides new tools for studying harmonic measures and Laplacian decompositions.
Findings
Decomposition of Laplacian into foliated and basic parts
Characterization of totally invariant measures
Differential equation for harmonic measure density
Abstract
In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foliation. The stochastic approach together with a proposed foliated vector calculus provide a natural method to work on harmonic measures. Other results include a decomposition of the Laplacian in terms of the foliated and basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures.
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Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Advanced Mathematical Modeling in Engineering