Estudo sobre estabilidade estocásticaa equação de Sagirow

Resumo

This dissertation investigates the stability of dynamical systems subject to uncertainties, governed by Stochastic Differential Equations (SDEs), focusing on the trajectory dynamics of satellites modeled by the Sagirow equation. With that purpose, we review notions of deterministic stability (Lyapunov, asymptotic, exponential) and stochastic stability (probability, p-th moment, and average exponential). In the theoretical core, we employ the stochastic Lyapunov method to deduce sufficient stability conditions for the trivial solution of the model. Furthermore, we conduct a systematic numerical study with Euler–Maruyama, Milstein, and their Tamed versions, evaluating which methods are capable of reproducing theoretical stability. The theorysimulation comparison delimits practical stability boundaries and highlights when classical methods fail by explosion, pointing out the advantages of Tamed variants. The results contribute verifiable stability criteria for the Sagirow equation and numerical guidelines for reliable simulation of SDEs.

Ficha do documento

Tipo

Dissertação

Ano

2025

Instituição

Fundação Getulio Vargas

Fonte

Repositório da FGV

Idioma

Português

Acesso

Acesso aberto

Identificador

oai:repositorio.fgv.br:10438/38180

Palavras-chave

SagirowLyapunovEuler-MaruyamaMilsteinEquações diferenciais estocásticasEstabilidadeMétodos TamedMatemáticaProcesso estocásticoEquações diferenciaisAnálise numéricaSistemas dinamicos diferenciais