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Random walks in a quarter plane with zero drifts. I: Ergodicity and null recurrence. (English) Zbl 0747.60064

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.

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
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