A bernoulli excursion and its various applications

This paper is concerned with a random walk process in which and for i = 1, 2, ···, 2n. This process is called a Bernoulli excursion. The main object is to find the distribution, the moments, and the asymptotic distribution of the random variable . n defined by . The results derived have various applications in the theory of probability, including random graphs, tournaments and order statistics.