arXiv subjects

Vincent Kagan

Publications and source records attributed to Vincent Kagan.

2 recordsLinked to original sources

arXiv2026

Averaging Principle for Ordinary Differential Equations in a Multiscale Random Environment

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.

math.PR↗

arXiv2025

Averaging principle for jump processes depending on fast ergodic dynamics

We consider a slow-fast stochastic process where the slow component is a jump process on a measurable index set whose transition rates depend on the position of the fast component. Between the jumps, the fast component evolves according to an ergodic dynamic in a state space determined by the index process. We prove that, when the ergodic dynamics are accelerated, the slow index process converges to an autonomous pure jump process on the index set. We apply our results to prove the convergence of a typed branching process toward a continuous-time Galton-Watson process, and of an epidemic model with fast viral loads dynamics to a standard contact process.

math.PR↗