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Conditions for recurrence and transience for one family of random walks
Vyacheslav M. Abramov · 2017-08-11 · via math.PR updates on arXiv.org

A parametric family of two-dimensional random walks $\mathbf{S}_t(a)$ $=\big(S_t^{(1)}(a),$ $S_t^{(2)}(a)\big)$ in the main quarter plane is studied. The components $S_t^{(1)}(a)$ and $S_t^{(2)}(a)$ are assumed to be correlated in the way that is defined exactly in the paper. We derive the conditions on $a$, under which a random walk $\mathbf{S}_t(a)$ is recurrent.

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