Wong–Zakai approximations for quasilinear systems of Itô’s type stochastic differential equations

We extend to the multidimensional case a Wong–Zakai-type theorem proved by Hu and Øksendal (1996) for scalar quasi-linear Itô stochastic differential equations (SDEs). More precisely, with aim of approximating solution quasilinear system Itô’s SDEs, we consider any finite partition time interval [0,T] equations, where Brownian motion is replaced its polygonal approximation product between diffusion coefficients smoothed white noise interpreted as Wick product. remark that in one dimensional this type can be reduced, means transformation related method characteristics, study random ordinary equation. Here, instead, naturally led investigation semilinear hyperbolic partial utilize constructing Wong–Zakai approximated systems. show law each element sequence solves sense distribution Fokker–Planck equation converges equation, mesh tends zero.