L. Shapiro has presented and solved a problem of a class of random walks with absorbing points on plane lattice points .[1]He divided the all lattice points on line y=x(x>0) into two classes by modulo 2, and select...L. Shapiro has presented and solved a problem of a class of random walks with absorbing points on plane lattice points .[1]He divided the all lattice points on line y=x(x>0) into two classes by modulo 2, and selected one of the two classes to be the set of absorbing points. In this paper,we generalize the Shapiro problem:divide the all lattice points on line y = x(x>0) into k classes by modulo k,and select one class or more classes of the k classes to be the set of absorbing points. We solve the generalized problem by using the residue method and give an application of it to probability theory.展开更多
文摘L. Shapiro has presented and solved a problem of a class of random walks with absorbing points on plane lattice points .[1]He divided the all lattice points on line y=x(x>0) into two classes by modulo 2, and selected one of the two classes to be the set of absorbing points. In this paper,we generalize the Shapiro problem:divide the all lattice points on line y = x(x>0) into k classes by modulo k,and select one class or more classes of the k classes to be the set of absorbing points. We solve the generalized problem by using the residue method and give an application of it to probability theory.
