Nonlinear effects within invariance principles
Abstract
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.
Cite
@article{arxiv.2402.13748,
title = {Nonlinear effects within invariance principles},
author = {Maximilian Engel and Peter K. Friz and Tal Orenshtein},
journal= {arXiv preprint arXiv:2402.13748},
year = {2024}
}
Comments
23 pages