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An averaging principle for stochastic differential equations

Grant number: 18/16568-0
Support Opportunities:Regular Research Grants
Duration: November 01, 2018 - October 31, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Fabiano Borges da Silva
Grantee:Fabiano Borges da Silva
Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil


This research project has as objective to study an averaging principle in the context of stochastic differential equations (SDE), whose perturbation on the (original) stochastic flow, generated by the EDE that preserves foliation of the manifold, that is, trajectories initiated on a particular leaf, remain on this leaf, is given by the vector field $ K $, transversal to the compact leaves that forms the manifold. For a given $\epsilon$ small enough, the behavior of the transversal system, with therescaled time given by $\frac{t}{\epsilon}$, is approximated by an ordinary differential equation (ODE) in the transversal space. Moreover, the vector field of this ODE is given by the ergodic average of the componentof $K$ on each leaf. We also intend to explore geometric properties of the manifold via this approximation technique for EDE, in order to find new results and applications. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
LEDESMA, DIEGO SEBASTIAN; BORGES DA SILVA, FABIANO. Decomposition of stochastic flow and an averaging principle for slow perturbations. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 35, n. 4, p. 625-654, . (15/07278-0, 18/16568-0, 12/18780-0)
LEDESMA, DIEGO SEBASTIAN; ANAYA, ROBERT ANDRES GALEANO; BORGES DA SILVA, FABIANO. Estimates for the volume variation of compact submanifolds driven by a stochastic flow. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. N/A, p. 27-pg., . (15/07278-0, 18/16568-0, 12/18780-0)
LUQUE JUSTO, CLAUDIA; LEDESMA, DIEGO SEBASTIAN; SILVA, FABIANO BORGES. An isometric embedding of the g(t)-Brownian motion with application in stability and homotopy group. Stochastics and Dynamics, v. 19, n. 6, . (15/07278-0, 12/18780-0, 18/16568-0)

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