Nunno, Giulia Di et Zhang, Tusheng, Approximations of stochastic partial differential equations, Annals of applied probability , 26(3), 2016, pp. 1443-1466
In this paper, we show that solutions of stochastic partial differential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic Burgers equations are discussed.