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Perron-Frobenius spectrum for random maps and its approximation. (English) Zbl 0996.37005
The author develops the spectral theory of the Perron-Frobenius (transfer) operator of random maps which acts in certain Banach spaces of generalized functions. The author considers contracting or expanding in average maps and shows stochastic stability of the corresponding Perron-Frobenius spectrum considering its finite rank approximations via “stochastically smoothed” Ulam’s approximation scheme.

MSC:
37A30 Ergodic theorems, spectral theory, Markov operators
37H10 Generation, random and stochastic difference and differential equations
37A25 Ergodicity, mixing, rates of mixing
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