Probabilities of landing on parallel lines, with natural coefficients of inclination
The author considers binomial random walks in a plane from the origin of a Cartesian coordinate system to points with nonnegative integer coordinates. The formulae are derived for hit probabilities on parallel straight lines determined by the equations \(y=kx+b_ 1\), \(y=k(x-b_ 2)\), \(y=k(x-b_ 2)-1,...\), \(y=k(x-b_ 2)-k+1\), where k, \(b_ 1\), and \(kb_ 2\) are natural numbers.
hit probabilities on parallel straight lines
scientific article; zbMATH DE number 3958385