We consider a centered random walk with finite variance and investigate the asymptotic behaviour of the probability that the area under this walk remains positive up to a large time n. Assuming that the moment of order 2+δ is finite, we show that the exact asymptotics for this probability is n−1/4. To show this asymptotics we develop a discrete potential theory for integrated random walks.
|Number of pages||26|
|Journal||l'Institut Henri Poincare. Annales (B). Probabilites et Statistiques|
|Publication status||Published - 14 Jan 2015|