Probabilistic Analysis of a Schröder Walk Generation Algorithm

Abstract

Using some tools from Combinatorics, Probability Theory, and Singularity analysis, we present a complete asymptotic probabilistic analysis of the cost of a Schroder walk generation algorithm proposed by Penaud et al.([13]).Such a walk S(.) is made of northeast, southeast and east steps, but each east step is made of two time units (if we consider recording the time t on the abscissa and the moves on the ordinates). The walk starts from the origin at time 0, cannot go under the time axis, and we add the constraint S(2n) = 0. Five different probability distributions will appear in the study: Gaussian, Exponential, Geometric, Rayleigh and a new probability distribution, that we can characterize by its density Laplace Transform and its moments.