Large deviation principle for slow-fast McKean-Vlasov SDEs

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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Publication Details

Journal
Scientia Sinica Mathematica
Published
2026-02-01
DOI
https://doi.org/10.1360/ssm-2025-0108
Primary Topic
Stochastic processes and financial applications
Type
article
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article

Large deviation principle for slow-fast McKean-Vlasov SDEs

Jie Ren, Xia Pengcheng
Scientia Sinica Mathematica
Stochastic processes and financial applications
article

Large deviation principle for slow-fast McKean-Vlasov SDEs

Jie Ren, Xia Pengcheng
article en

Abstract

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.

Scientia Sinica Mathematica
Openalex Percentile: Top 68%
Stochastic processes and financial applications
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Large deviation principle for slow-fast McKean-Vlasov SDEs — Jie Ren, Xia Pengcheng · Scientia Sinica Mathematica (2026) | TGRS Research Map | TGRS