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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Foliated stochastic calculus: Harmonic measures
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by Pedro J. Catuogno, Diego S. Ledesma and Paulo R. Ruffino PDF
Trans. Amer. Math. Soc. 368 (2016), 563-579 Request permission

Abstract:

In this article we present an intrinsic construction of foliated Brownian motion (FoBM) via stochastic calculus adapted to a foliated Riemannian manifold $(M, \mathcal {F})$. The stochastic approach together with this proposed foliated vector calculus provide a natural method to work with (L. Garnett’s) harmonic measures in $M$. New results include, beside an explicit stochastic equation for the FoBM, a decomposition of the Laplacian of $M$ in terms of the foliated and the basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures.
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  • Pedro J. Catuogno
  • Affiliation: Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970 - Campinas - SP, Brazil
  • Email: pedrojc@ime.unicamp.br
  • Diego S. Ledesma
  • Affiliation: Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970 - Campinas - SP, Brazil
  • Email: dledesma@ime.unicamp.br
  • Paulo R. Ruffino
  • Affiliation: Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970 - Campinas - SP, Brazil
  • ORCID: 0000-0002-6524-2508
  • Email: ruffino@ime.unicamp.br
  • Received by editor(s): August 1, 2012
  • Received by editor(s) in revised form: November 22, 2013
  • Published electronically: April 24, 2015
  • Additional Notes: The first author’s research was partially supported by FAPESP 11/50151-0 and 12/18780-0.
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 563-579
  • MSC (2010): Primary 58J65, 53C12; Secondary 60H30, 60J60
  • DOI: https://doi.org/10.1090/tran/6431
  • MathSciNet review: 3413874