Martingale approach to subexponential asymptotics for random walks

Denis Denisov, Vitali Wachtel

    Research output: Contribution to journalArticlepeer-review

    28 Downloads (Pure)


    Consider the random walk S n = ξ 1+,..., + ξ n with independent and identically distributed increments and negative mean Eξ = - m <0. Let M = sup 0 x),x → ∞ for long-tailed distributions. This derivation is based on the martingale arguments and does not require any prior knowledge of the theory of long-tailed distributions. In addition the same approach allows to obtain asymptotics for P(M τ > x), where M τ = max 0<i<τ S i and τ = min{n ≥ 1: S n ≤ 0}.
    Original languageEnglish
    Pages (from-to)1-9
    Number of pages8
    JournalElectronic Communications in Probability
    Publication statusPublished - 2012


    • Cycle maximum
    • Heavy-tailed distribution
    • Random walk
    • Stopping time
    • Supremum


    Dive into the research topics of 'Martingale approach to subexponential asymptotics for random walks'. Together they form a unique fingerprint.

    Cite this