Skip to main content

Moments for first-passage and last-exit times, the minimum, and related quantities for random walks with positive drift

  • Svante Janson (a1)

Consider the sequence of partial sums of a sequence of i.i.d. random variables with positive expectation.

We study various random quantities defined by the sequence of partial sums, e.g. the time at which the first or last crossing of a given level occurs, the value of the partial sum immediately before or after the crossing, the minimum of all partial sums. Necessary and sufficient conditions are given for the existence of moments of these quantities.

Hide All
Chow, Y. S. and Lai, T. L. (1975) Some one-sided theorems on the tail distribution of sample sums with applications to the last time and largest excess of boundary crossings. Trans. Amer. Math. Soc. 208, 5172.
Chow, Y. S. and Lai, T. L. (1979) Moments of ladder variables for driftless random walks. Z. Wahrscheinlichkeitsth. 48, 253257.
Doney, R. A. (1980) Moments of ladder heights in random walks. J. Appl. Prob. 17, 248252.
Feller, W. (1966) An Introduction to Probability Theory and its Applications II. Wiley, New York.
Gut, A. (1974) On the moments and limit distributions of some first passage times. Ann. Prob. 2, 277308.
Gut, A. (1986) Stopped Random Walks. Limit Theorems and Applications. To appear.
Hunt, R. A. (1966) On L(p, q) spaces. Enseignement Math. 12, 249275.
Kiefer, J. and Wolfowitz, J. (1956) On the characteristics of the general queueing process, with applications to random walk. Ann. Math. Statist. 27, 147161.
Prabhu, N. U. (1965) Stochastic Processes. Macmillan, New York.
Smith, W. L. (1967) A theorem on functions of characteristic functions and its applications to some renewal random walk problems. Proc. 5th Berkeley Symp. Math. Statist. Prob. 2, 265309.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *