Exit times for integrated random walks

Denis Denisov, Vitali Wachtel

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    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.
    Original languageEnglish
    Pages (from-to)167-193
    Number of pages26
    Journall'Institut Henri Poincare. Annales (B). Probabilites et Statistiques
    Issue number1
    Publication statusPublished - 14 Jan 2015


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