Polynomial rates via deconvolution for nonparametric estimation in McKean-Vlasov SDEs

• 成果类型: Article
• 署名作者: Amorino, Chiara; Belomestny, Denis; Pilipauskaite, Vytaute; Podolskij, Mark; Zhou, Shi-Yuan
• 署名单位: Pompeu Fabra University; Barcelona School of Economics; Aalborg University; University of Luxembourg
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01346-5
• 发表日期: 2025
• 页码: 539-584
• 关键词: granular media equations; parametric inference; small variance; MODEL; propagation

摘要

This paper investigates the estimation of the interaction function for a class of McKean-Vlasov stochastic differential equations. The estimation is based on observations of the associated particle system at time T, considering the scenario where both the time horizon T and the number of particles N tend to infinity. Our proposed method recovers polynomial rates of convergence for the resulting estimator. This is achieved under the assumption of exponentially decaying tails for the interaction function. Additionally, we conduct a thorough analysis of the transform of the associated invariant density as a complex function, providing essential insights for our main results.