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NONLINEAR EFFECTS WITHIN INVARIANCE PRINCIPLES
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DOI：10.3934/cpaa.2026046.png)
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Abstract
En 中文
. We study invariance principles in the rough path topology for stationary discrete and continuous time processes. Simple second moment computations give explicit Green-Kubo-type formulas for both the covariance and the linear correction, called the area anomaly, of the iterated integral of the limiting Brownian motion. A key observation is that the area anomaly admits a structural description: it is the antisymmetric part of the relevant Green- Kubo expression. This provides a unified explanation of area corrections that appear in several different frameworks, including Markovian, regenerative, and deterministic fast-slow models, and highlights a common mechanism underlying results that previously arose from model-specific arguments.
Keywords:
Invariance principles
rough paths
area anomaly
Green-Kubo formulas
iterated integrals
Wong-Zakai limits
stationary processes
fast-slow systems
diffusion limits
regenerative processes
Journal
C
IF:
0.9
Papers:
88
Citations:
0
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Cited Papers