Fayolle, G.; Malyshev, V. A.; Menshikov, M. V. Random walks in a quarter plane with zero drifts. I: Ergodicity and null recurrence. (English) Zbl 0747.60064 Ann. Inst. Henri Poincaré, Probab. Stat. 28, No. 2, 179-194 (1992). Summary: We solve the problem of non ergodicity and null recurrence for random walks in the quarter plane with zero drifts in the interior of the domain. A general criterion for null recurrence is given and then used to construct sub- and supermartingales by means of Lyapunov functions, which are here functionals of quadratic forms. Cited in 8 Documents MSC: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60G50 Sums of independent random variables; random walks 60G07 General theory of stochastic processes Keywords:problem of non ergodicity; random walks; criterion for null recurrence; Lyapunov functions PDFBibTeX XMLCite \textit{G. Fayolle} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 28, No. 2, 179--194 (1992; Zbl 0747.60064) Full Text: Numdam EuDML