Limit theorems for compositions of random operators and differential equations corresponding to the limit processes

The sequences of compositions of independent identically distributed random operators are studied as the noncommutative analog of the sequences of sum of vector valued random variables. The analog of law of large numbers is obtained for compositions of random one-parametric semigroups. The generalization of weak convergence of the sequence of measures on a Banach space is introduced. By means of this type of convergence the limit theorems for the sequences of compositions of independent random mappings in a Hilbert space are obtained. Differential equations describing the orbits of the limit semigroups are studied.