Analysis of the large deviation principle in Hilfer fractional stochastic differential equations, suggesting new insights into system behavior with noise perturbation.
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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Chen et al. (2025) studied this question.
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