The paper deals with convergence of solutions of a class of stochastic differential equations driven by infinite-dimensional semimartingales. The infinite dimensional semimartingales considered in the paper are Hilbert-space valued. The theorems presented generalize the convergence result obtained by Wong and Zakai for stochastic differential equations driven by linear interpolations of a finite-dimensional Brownian motion. In particular, a general form of the correction factor is derived. Examples are given illustrating the use of the theorems to obtain other kinds of approximation results.
"Wong-Zakai type convergence in infinite dimensions." Electron. J. Probab. 18 1 - 34, 2013. https://doi.org/10.1214/EJP.v18-2650