Geodesic
On the law of large numbers for compositions of independent random semigroups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 86-91

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We study random linear operators in Banach spaces and random one-parameter semigroups of such operators. For compositions of independent random semigroups of linear operators in the Hilbert space we obtain sufficient conditions for fulfilment of the law of large numbers and give examples of its violation.
Keywords: law of large numbers, random map, random semigrop, Chernoff theorem. 
@article{IVM_2016_10_a11,
     author = {V. Zh. Sakbaev},
     title = {On the law of large numbers for compositions of independent random semigroups},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {86--91},
     publisher = {mathdoc},
     number = {10},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_10_a11/}
}
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V. Zh. Sakbaev. On the law of large numbers for compositions of independent random semigroups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 86-91. http://geodesic.mathdoc.fr/item/IVM_2016_10_a11/