Komashko, O. V. The generalized potential of a certain Markov chain. (English. Russian original) Zbl 0738.60065 Theory Probab. Math. Stat. 43, 77-79 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 43, 69-72 (1990). Summary: An investigation is made of the domain of definition of the generalized potential of a Markov chain corresponding to a linear homeomorphism of the circle that is transient in the Harris sense and is not irreducible. It is proved that in the space of absolutely continuous measures with continuous density the generalized potential can be defined as the sum of a series consisting of powers of the transition operator. MSC: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 31C99 Generalizations of potential theory Keywords:generalized potential of a Markov chain; transient in the Harris sense; powers of the transition operator PDFBibTeX XMLCite \textit{O. V. Komashko}, Theory Probab. Math. Stat. 43, 77--79 (1990; Zbl 0738.60065); translation from Teor. Veroyatn. Mat. Stat., Kiev 43, 69--72 (1990)