Conditions for recurrence and transience for one family of random walks

Abstract

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.