Decomposition of flows in averaging principles and stochastic transport equation
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Stochastic dynamics: analytical and geometrical aspects with applications
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An introduction to stochastic differential equations and stochastic flow of diffeomorphisms in smooth manifolds
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| Author(s): |
Amanda Silvieri Leite de Oliveira
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Presidente Prudente. 2021-07-20. |
| Institution: | Universidade Estadual Paulista (Unesp). Faculdade de Ciências e Tecnologia. Presidente Prudente |
| Defense date: | 2021-06-25 |
| Advisor: | Fabiano Borges da Silva |
| Abstract | |
In this work, we initially present a brief review of the contents of stochastic calculus that allow the introduction of stochastic differential equations and some of their applications and motivations. As the main objective of this work, we study the stochastic differential equations on smooth manifolds and the Itô Formula for action of stochastic flows on vector fields and differential forms. Finally, we study under which conditions a stochastic flow preserves a volume form following the approach presented in Kunita (1982) (AU) | |
| FAPESP's process: | 19/08076-2 - Stochastic flows on manifolds |
| Grantee: | Amanda Silvieri Leite de Oliveira |
| Support Opportunities: | Scholarships in Brazil - Master |