Geodesic
On the convergence of infinite products of independent random linear operators in a~Hilbert space
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 4, pp. 808-813

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The first two theorems of the paper give simple sufficient conditions for the convergence with probability 1 of the products named in the title. The third theorem presents necessary and sufficient conditions for convergence and resembles the well-known Kolmogorov's theorem on three series. 
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     author = {T. {\CYRA}. Skorohod},
     title = {On the convergence of infinite products of independent random linear operators in {a~Hilbert} space},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {808--813},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a9/}
}
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T. А. Skorohod. On the convergence of infinite products of independent random linear operators in a~Hilbert space. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 4, pp. 808-813. http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a9/