• Maximum on a random time interval of a random walk with infinite mean

      Denisov, Denis; orcid: 0000-0003-0025-7140; email: denis.denisov@manchester.ac.uk (Springer US, 2020-06-23)
      Abstract: Let ξ1, ξ2, … be independent, identically distributed random variables with infinite mean E[|ξ1|]=∞. Consider a random walk Sn=ξ1+⋯+ξn, a stopping time τ=min{n≥1:Sn≤0} and let Mτ=max0≤i≤τSi. We study the asymptotics for P(Mτ>x), as x→∞.