Recurrence of two-dimensional queueing processes, and random walk exit times from the quadrant
Recurrence of two-dimensional queueing processes, and random walk exit times from the quadrant
Let X=(X1,X2) be a two-dimensional random variable and X(n), n∈N, a sequence of i.i.d. copies of X. The associated random walk is S(n)=X(1)+⋯+X(n). The corresponding absorbed-reflected walk W(n), n∈N, in the first quadrant is given by W(0)=x∈R+2 and W(n)=max{0,W(n−1)−X(n)}, where the maximum is taken coordinate-wise. This is often called the …