Abstract
Under a Lipschitz condition on distribution dependent coefficients, the central limit theorem and the moderate deviation principle are obtained for solutions of McKean-Vlasov type stochastic differential equations, which generalize the corresponding results for classical stochastic differential equations to the distribution dependent setting.
Highlights
In recent years, McKean-Vlasov stochastic differential equations (MV-SDEs for short) have received increasing attentions by researchers
They are called as mean-field SDEs or distribution dependent SDEs which are much more involved than classical SDEs as the drift and diffusion coefficients depending on the solution and the law of solution
The analysis of stochastic particle systems has developed as crucial mathematic tools modelling economic and finance systems
Summary
McKean-Vlasov stochastic differential equations (MV-SDEs for short) have received increasing attentions by researchers They are called as mean-field SDEs or distribution dependent SDEs which are much more involved than classical SDEs as the drift and diffusion coefficients depending on the solution and the law of solution. In a nutshell, this kind of equations play important roles in characterising non-linear Fokker-Planck equations and environment dependent financial systems, see [9, 10, 12, 13, 20, 23, 24] and references therein. There are two main approaches to investigate LDPs, one is weak convergence method, the other one is based on exponential approximation argument
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