FOLIATED STOCHASTIC CALCULUS: HARMONIC MEASURES

Autor(es)

Catuogno, Pedro J. ; Ledesma, Diego S. ; Ruffino, Paulo R.

• Tipo de documento: Artigo Científico
• Fonte: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 368, n. 1, p. 17-pg., 2016-01-01.

Resumo

In this article we present an intrinsic construction of foliated Brownian motion (FoBM) via stochastic calculus adapted to a foliated Riemannian manifold (M, 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. (AU)

• Processo FAPESP: 12/18780-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 11/50151-0 - Fenômenos dinâmicos em redes complexas: fundamentos e aplicações
• Beneficiário: Elbert Einstein Nehrer Macau
• Modalidade de apoio: Auxílio à Pesquisa - Temático