Convergence rate for moderate interaction particles and application to mean field games

Autor(es)

Knorst, Josue ; Olivera, Christian ; de Souza, Alexandre B.

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 549, n. 2, p. 20-pg., 2025-05-02.

Resumo

We study two interacting particle systems, both modeled as a system of N stochastic differential equations driven by Brownian motions with singular kernels and moderate interaction. We show a quantitative result where the convergence rate depends on the moderate scaling parameter, the regularity of the solution of the limit equation and the dimension. Our approach is based on the techniques of stochastic calculus, some properties of Besov and Triebel-Lizorkin space, and the semigroup approach introduced in [12]. New techniques are presented to address the difficulty arising from the nonlinear term. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU)

• Processo FAPESP: 22/13413-0 - Decomposição de fluxos em princípios de média e equação de transporte estocástico
• Beneficiário: Josué Knorst
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 20/04426-6 - Dinâmica estocástica: aspectos analíticos, geométricos e aplicações
• Beneficiário: Paulo Regis Caron Ruffino
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 22/03379-0 - Análise estocástica e determinística para modelos irregulares
• Beneficiário: Christian Horacio Olivera
• Modalidade de apoio: Auxílio à Pesquisa - Regular