A stochastic evolution equation arising from the fluctuation of a class of interacting particle systems
- Kurtz, Thomas G.
- Xiong, Jie
2010 Mathematics Subject Classification
- 60H15 60H35 60B12 60F17 60F25 60H10 93E11
- Stochastic partial differential equations, interacting infinite particle system, central limit theorem, Euler scheme
In an earlier paper, we studied the approximation of solutions $V(t)$ to a class of SPDEs by the empirical measure $V^n(t)$ of a system of $n$ interacting diffusions. In the present paper, we consider a central limit type problem, showing that $sqrt n(V^n-V)$ converges weakly, in the dual of a nuclear space, to the unique solution of a stochastic evolution equation. Analogous results in which the diffusions that determine $V^n$ are replaced by their Euler approximations are also discussed.