Autor(es)

Ledesma, Diego Sebastian ; Anaya, Robert Andres Galeano ; Borges da Silva, Fabiano

• Tipo de documento: Artigo Científico
• Fonte: DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. N/A, p. 27-pg., 2022-06-07.

Resumo

Consider a compact submanifold N without the boundary of a Riemannian manifold M, and a stochastic flow phi(t) - associated with a stochastic differential equation. Let N-t = phi(t) (N) be the random compact submanifold obtained by the action of the stochastic flow. In this work, we present an Ito formula for the volume of the random variable N-t and, as a main result, we obtain estimates for its average growth assuming that Ricci curvature is bounded. We first analyse the particular case where the submanifolds are closed curves, thus obtaining estimates for the arc length, and then we study the volume variation of compact submanifolds of dimensions greater than or equal to 2. In addition, we apply our results to the special case where the vector fields of stochastic differential equation are conformal Killing. (AU)

• Processo FAPESP: 15/07278-0 - Dinâmica estocástica: aspectos analíticos, geométricos e aplicações
• Beneficiário: Paulo Regis Caron Ruffino
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 18/16568-0 - Um princípio de médias para equações diferenciais estocásticas
• Beneficiário: Fabiano Borges da Silva
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• 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