Abstract
Limit properties of the convolution sequence of a regular measure on a compact topological semigroup are examined in this paper. Similar questions, as they arise in the case of a compact group, were examined by KaWaDa & Ito [4]. Recently Bellman [1] and GRenaNdeR [3] considered special limit theorems for products of independent identically distributed random operators. Such problems are closely related to those in this paper. It should be noted that similar questions arise when considering the structure of stationary stochastic processes [7]. Various results on compact semigroups are used in characterizing the class of limit measures [5], [6], [8].
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Davis, R.A., Lii, KS., Politis, D.N. (2011). Limits of Convolution Sequences of Measures on a Compact Topological Semigroup. In: Davis, R., Lii, KS., Politis, D. (eds) Selected Works of Murray Rosenblatt. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8339-8_19
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DOI: https://doi.org/10.1007/978-1-4419-8339-8_19
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