arXiv subjects
Publications and source records attributed to Chungang Shi.
An approximation is derived for a Langevin equation with distribution-dependent potential and state-dependent, randomly fast oscillation. By some estimates and a diffusion approximation the limiting equation is shown to be distribution-dependent stochastic differential equation (SDEs) driven by white noise.
The small mass limit is derived for a McKean-Vlasov equation with state-dependent friction in $d$-dimensional space. By applying the averaging approach to a non-autonomous slow-fast system with the microscopic and macroscopic scales, the convergence in distribution is obtained.
In the paper, a class of second-order McKean-Vlasov stochastic evolution equation driven by Poisson jumps with non-Lipschitz conditions is considered. The existence and uniqueness of the mild solution is established by means of the Carath${\rm \acute{e}}$odory approximation technique. Furthermore, an averaging principle is obtained between the solution of the second-order McKean-Vlasov stochastic evolution equation and that of the simplified equation in mean square sense.
The small mass limit is derived for a McKean-Vlasov equation subject to environmental noise with state-dependent friction. By applying the averaging approach to a non-autonomous stochastic slow-fast system with the microscopic and macroscopic scales, the convergence in distribution is obtained.
In the paper, the Kolmogorov distance is used to study the Smoluchowski-Kramers approximation for diffusions with jumps. The convergence rate is derived by Malliavin calculus.