March 3, 2026Open Access

Large deviation principle for slow-fast McKean-Vlasov SDEs

Puntos clave

The large deviation principle indicates how certain stochastic dynamics behave under rare fluctuations, enhancing our understanding of system stability.
Key findings are established for systems where noise intensity approaches zero, particularly highlighting distributional dependencies.
Main techniques employed are the Poisson equation and weak convergence to derive the large deviation principle effectively.
This framework offers insights into complex stochastic processes, motivating further exploration in related systems and applications.

Resumen

In this paper, we prove the Freidlin-Wentzell-type large deviation principle for a general system of fully-coupled slow-fast McKean-Vlasov stochastic dynamics, when the noise intensity δ→0 and the time scale parameter varepsilon(δ) satisfies varepsilon²(δ)/δ→0. The coefficients can depend on the distribution of the slow motion and that of the fast motion. The main techniques are based on the Poisson equation and the weak convergence approach for the large deviation principle.

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