August 19, 2025Open Access

Large Deviation Principle for Hilfer Fractional Stochastic McKean–Vlasov Differential Equations

Key Points

The study establishes a large deviation principle for stochastic McKean–Vlasov equations affected by noise.
Key evidence shows the application of Laplace transforms leading to significant mathematical results.
Using weak convergence methods, the approach connects LDP with behavioral analysis under perturbations.
Findings highlight implications for further research on noisy systems and the dynamics of stochastic differential equations.

Abstract

This paper studies the large deviation principle (LDP) of a class of Hilfer fractional stochastic McKean–Vlasov differential equations with multiplicative noise. Firstly, by making use of the Laplace transform and its inverse transform, the solution of the equation is derived. Secondly, considering the equivalence between the LDP and the Laplace principle (LP), the weak convergence method is employed to prove that the equation satisfies the LDP. Finally, through specific example, it is elaborated how to utilize the LDP to analyze the behavioral characteristics of the system under small noise perturbation.

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