Central limit type theorem and large deviation principle for multi-scale McKean–Vlasov SDEs
Central limit type theorem and large deviation principle for multi-scale McKean–Vlasov SDEs
复制标题
DOI：
10.1007/s00440-023-01214-8
复制
发表时间：
2021-12
影响因子：
2
通讯作者：
Wei Hong;Shihu Li;Wei Liu;Xiaobin Sun
中科院分区：
文献类型：
--
作者：
Wei Hong;Shihu Li;Wei Liu;Xiaobin Sun
The main aim of this work is to study the asymptotic behavior for multi-scale McKean–Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e. the deviation between the slow componentand the solutionof the averaged equation converges weakly to a limiting process. More precisely,converges weakly into the solution of certain distribution dependent stochastic differential equation, which involves an extra explicit stochastic integral term. Secondly, in order to estimate the probability of deviations away from the limiting process, we further investigate the Freidlin–Wentzell’s large deviation principle for multi-scale McKean–Vlasov stochastic system when the small-noise regime parameterand the time scale parametersatisfies. The main techniques are based on the Poisson equation for central limit type theorem and the weak convergence approach for large deviation principle.
