On the existence of strong solutions of linear stochastic differential equations in $\mathbb{R}^\infty$

In this work we prove the existence of a strong solution of a linear stochastic differential equation in $\mathbb R^\infty$. We use an infinite-dimensional modification of the method of successive approximations to find a solution to systems of a special form as well as an analogue of the Jordan method of reducing a matrix to a block form. The nonuniqueness of the constructed solution is shown.