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# An averaging principle for stochastic differential equations

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

Abstract

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)