Let θ(a) be the first time when the range (Rm;n≥0) is equal to a, Rn being equal to the difference of the maximum and the minimum, taken at time n, of a simple random walk on ℝ. The paper computes the g.f. of θ(a); this allows us to compute the distributions of θ(a) and Rn. It also investigates the asymptotic behaviour of θ(n), n going to infinity.
