ROUGH MCKEAN-VLASOV DYNAMICS FOR ROBUST ENSEMBLE KALMAN FILTERING

• 成果类型: Article
• 署名作者: Coghi, Michele; Nilssen, Torstein; Nuesken, Nikolas; Reich, Sebastian
• 署名单位: University of Trento; University of Agder; University of London; King's College London; University of Potsdam
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1957
• 发表日期: 2023
• 页码: 5693-5752
• 关键词: STATISTICAL-INFERENCE; parametric-estimation; propagation; sdes; REPRESENTATIONS; approximation; CONVERGENCE; DIFFUSIONS; reduction; STABILITY

摘要

Motivated by the challenge of incorporating data into misspecified and multiscale dynamical models, we study a McKean-Vlasov equation that contains the data stream as a common driving rough path. This setting allows us to prove well-posedness as well as continuity with respect to the driver in an appropriate rough-path topology. The latter property is key in our subsequent development of a robust data assimilation methodology: We establish propagation of chaos for the associated interacting particle system, which in turn is suggestive of a numerical scheme that can be viewed as an extension of the ensemble Kalman filter to a rough-path framework. Finally, we discuss a data-driven method based on subsampling to construct suitable rough path lifts and demonstrate the robustness of our scheme in a number of numerical experiments related to parameter estimation problems in multiscale contexts.