Geodesic
On the existence of strong solutions of linear stochastic differential equations in $\mathbb{R}^\infty$
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 4, pp. 826-831

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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. 
@article{TVP_1997_42_4_a13,
     author = {Yu. V. Mednitskii},
     title = {On the existence of strong solutions of linear stochastic differential equations in $\mathbb{R}^\infty$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {826--831},
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_4_a13/}
}
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Yu. V. Mednitskii. On the existence of strong solutions of linear stochastic differential equations in $\mathbb{R}^\infty$. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 4, pp. 826-831. http://geodesic.mathdoc.fr/item/TVP_1997_42_4_a13/