Mathematical analysis demonstrates deviation principles and limit theorems for small-noise Volterra McKean-Vlasov systems, highlighting limiting processes driven by the Lions derivative.
This work is devoted to studying asymptotic behaviors for Volterra type McKean-Vlasov stochastic differential equations with small noise. By applying the weak convergence approach, we establish the large and moderate deviation principles. In addition, we obtain the central limit theorem and find the Volterra integral equation satisfied by the limiting process, which involves the Lions derivative of the drift coefficient.
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Gao et al. (2026) studied this question.
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