Stability of mean-field stochastic differential equations under sublinear expectation

Sainan Wang; Sainan Wang

doi:10.3934/math.20261160

AIMS Mathematics

2026, Volume 11, Issue 9: 29179-29197. doi: 10.3934/math.20261160

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Research article

Stability of mean-field stochastic differential equations under sublinear expectation

Sainan Wang ^,

College of Artificial Intelligence, Zhejiang A & F University, Hangzhou 311300, China

Received: 08 June 2026 Revised: 20 August 2026 Accepted: 28 August 2026 Published: 10 September 2026
MSC : 34A12; 34A37; 34D05

This paper explores the properties of exponential decay and logarithmic decay in mean-field stochastic differential equations driven by G-Brownian motion. Using the distribution-dependent G-Lyapunov function approach, we derive explicit criteria for moment exponential stability and partial moment stability under general decay rates. By integrating moment estimation techniques, we also furnish analyzed formulas to compute the decay exponents. As an application, we present two examples to verify our results.
- mean-field stochastic differential equations,
- stability,
- G-Itô's formula
Citation: Sainan Wang. Stability of mean-field stochastic differential equations under sublinear expectation[J]. AIMS Mathematics, 2026, 11(9): 29179-29197. doi: 10.3934/math.20261160

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Abstract

This paper explores the properties of exponential decay and logarithmic decay in mean-field stochastic differential equations driven by G-Brownian motion. Using the distribution-dependent G-Lyapunov function approach, we derive explicit criteria for moment exponential stability and partial moment stability under general decay rates. By integrating moment estimation techniques, we also furnish analyzed formulas to compute the decay exponents. As an application, we present two examples to verify our results.

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