| Full text | |
| Author(s): |
Ledesma, Diego Sebastian
;
Anaya, Robert Andres Galeano
;
Borges da Silva, Fabiano
Total Authors: 3
|
| Document type: | Journal article |
| Source: | DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. N/A, p. 27-pg., 2022-06-07. |
| Abstract | |
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) | |
| FAPESP's process: | 15/07278-0 - Stochastic dynamics: analytical and geometrical aspects with applications |
| Grantee: | Paulo Regis Caron Ruffino |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 18/16568-0 - An averaging principle for stochastic differential equations |
| Grantee: | Fabiano Borges da Silva |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 12/18780-0 - Geometry of control systems, dynamical and stochastics systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |