Integral conditions for the invertibility of Markov chains on a half-line with general measure of irreducibility

We present conditions for the invertibility of Markov chains with values from ⁺ and general measure of irreducibility. The results are obtained by the classical method of test functions combined with the method of perturbation of partial potentials.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 705–712, May, 2004.