STATISTICAL PROPERTIES OF ENDOMORPHISMS AND COMPACT GROUP EXTENSIONS
STATISTICAL PROPERTIES OF ENDOMORPHISMS AND COMPACT GROUP EXTENSIONS
The statistical properties of endomorphisms under the assumption that the associated Perron–Frobenius operator is quasicompact are considered. In particular, the central limit theorem, weak invariance principle and law of the iterated logarithm for sufficiently regular observations are examined. The approach clarifies the role of the usual assumptions of ergodicity, weak …