First-passage time asymptotics over moving boundaries for random walk bridges

Article, Preprint English OPEN
Sloothaak, F.; Wachtel, Vitali; Zwart, Bert;
  • Related identifiers: doi: 10.1017/jpr.2018.39
  • Subject: Random walk | Mathematics(all) | first-passage time | Mathematics - Probability | Statistics, Probability and Uncertainty | Statistics and Probability | bridge | moving boundary

We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a re... View more
  • References (19)
    19 references, page 1 of 2

    [1] F. Aurzada and T. Kramm. The first passage time problem over a moving boundary for asymptotically stable le´vy processes. Journal of Theoretical Probability, 29(3):737-760, 2016.

    [2] E. Bolthausen. On a functional central limit theorem for random walks conditioned to stay positive. The Annals of Probability, 4(3):480-485, 06 1976.

    [3] F. Caravenna and L. Chaumont. An invariance principle for random walk bridges conditioned to stay positive. Electronic Journal of Probability, 18:1-32, 2013.

    [4] D. Denisov, A. Sakhanenko, and V. Wachtel. First passage times for random walks with non-identically distributed increments. arXiv:1611.00493.

    [5] D. Denisov and V. Shneer. Asymptotics for the first passage times of le´vy processes and random walks. Journal of Applied Probability, 50(1):6484, 2013.

    [6] I. Dobson, B. A. Carreras, and D. E. Newman. A branching process approximation to cascading loaddependent system failure. In 37th HICSS, 2004.

    [7] R. A. Doney. Conditional limit theorems for asymptotically stable random walks. Probability Theory and Related Fields, 70(3):351-360, 1985.

    [8] R. A. Doney. Local behaviour of first passage probabilities. Probability Theory and Related Fields, 152(3):559-588, 2012.

    [9] M.D. Donsker. An Invariance Principle for Certain Probability Limit Theorems. American Mathematical Society. Memoirs. 1951.

    [10] R. T. Durrett, D. L. Iglehart, and D. R. Miller. Weak convergence to brownian meander and brownian excursion. The Annals of Probability, 5(1):117-129, 02 1977.

  • Metrics
Share - Bookmark