On the straight line crossing problem for two-dimensional random walks

We investigate the first-crossing-time problem through unit-slope straight lines for a two-dimensional random walk whose single-step probabilities are symmetrically related. The transition probabilities conditioned by non-absorbtion at unit-slope straight lines and the first-crossing probabilities through such boundaries are expressed in term of the transition probabilities in the absence of boundaries. The probabilities of ultimate crossing are also given. An application to population models is finally indicated