In this paper we consider a stochastic differential equation with two independent Wiener processes in an infinite-dimensional Hilbert space. This equation can be a mathematical model of a dynamic system in the presence of several independent perturbing random factors. To study the parameters of this equation, the Daletsky-Trotter method of multiplicative representations is used. This method is applied to both deterministic and stochastic equations. The method consists in the following: one constructs a partition of the interval of existence of the solution [t0, T] into elementary [tk+1, tk]. On each elementary segment, the evolutionary resolving operator of the complete equation S(tk+1, tk) is considered, as well as the product of the resolving operators of equations that are fragments of the complete equation =Q1k×S1k×S2k
 Thus, two multiplicative families consisting of different resolving operators are compared. When the equivalence conditions, which are verified in this paper, are satisfied, it can be argued that the solution of a stochastic equation can, in a certain sense, be represented as a composition of the corresponding solutions of differential equations on elementary intervals, the right parts of which are drift, and, accordingly, diffusion.
 Moreover, in order to implement such a multiplicative scheme in the case of several independent Wiener processes, additional requirements regarding diffusion coefficients should be imposed. Namely: the diffusion coefficients must be commuting operators, continuous in time.
 The scheme of multiplicative representations is based on the study of the parameters of evolutionary families of decision operators, as well as their estimates in the norms of the corresponding spaces. In this case, to obtain a certain estimate, several iteration steps are considered for the corresponding equations in the Hilbert space. It should be noted that the scheme of multiplicative representations can be interpreted as a scheme for obtaining an approximate solution.