Nonlinear effects within invariance principles
| Autor: | Engel, Maximilian, Friz, Peter K., Orenshtein, Tal |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | The combination of functional limit theorems with the pathwise analysis of deterministic and stochastic differential equations has proven to be a powerful approach to the analysis of fast-slow systems. In a multivariate setting, this requires rough path ideas, as already suggested in the seminal work [Melbourne-Stuart, Nonlinearity, 24, 2011]. This initiated a program pursued by numerous authors and which has required substantial results on invariance principles (also known as functional central limit theorems) in rough path topologies. We take a unified point of view and provide simple and exact formulas, of the Green-Kubo type, that characterize the relevant Brownian rough path limits and discuss how they naturally apply in different settings. Comment: 23 pages |
| Databáze: | arXiv |
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