Year: 2026
Type: preprint
Abstract: We study slow-fast stochastic systems in which a fast process, evolving within several ergodic components, drives the transition rates of a slow jump process switching between these components. Considering a differential equation whose vector field depends on both processes, we show that, under suitable ergodicity and regularity conditions, its solutions converge in law in $D([0,T],\mathbb R^d)$ to an averaged system depending only on the slow process. The averaged drift is obtained by averaging the original vector field over the invariant measure of the fast process within each component. Our results extend classical averaging theory to systems where the vector field is explicitly influenced by a fast random environment with multi-component dynamics.
Source: arXiv (Cornell University)
Author: Kagan, Vincent
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7172386754
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