A global approach to first passage times

• Autorzy: Larsson-Cohn, L.
• Języki publikacji: EN

Abstrakty

EN

First passage times for discrete-time stochastic processes are studied from a global point of view, in terms of a mapping that takes a numerical sequence to its first passage time function. The continuity properties of this mapping with respect to Skorohod’s J₁ and M₁ topologies are examined. One typically has continuity in M₁, but in J₁ only under extra assumptions. The results are applied to random walks and renewal theory.

Słowa kluczowe

EN

stochastic processes; terms of a mapping; first passage time function

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 2
• Strony: 337--341
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Larsson-Cohn, L.

• Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden,

Bibliografia

• [1] P. Billingsley, Convergence of Probability Measures, Wiley, New York 1968.
• [2] D. L. Cohn, Measure Theory, Birkhäuser, Boston; Mass., 1980.
• [3] A. Gut, First passage times for perturbed random walks, Sequential Anal. 11 (1992), pp. 149-179.
• [4] T. L. Lai and D. Siegmund, A non-linear renewal theory with applications to sequential analysis I, Ann. Statist. 5 (1977), pp. 946-954.
• [5] T. L. Lai and D. Siegmund, A non-linear renewal theory with applications to sequential analysis II, Ann. Statist. 7 (1979), pp. 60-76.
• [6] L. Larsson-Cohn, Some limit and continuity theorems for perturbed random walks, Technical Report 1999: 2, Dept, of Mathematics, Uppsala University, 1999.
• [7] T. Lindvail, Weak convergence of probability measures and random functions in the function space D [0, ∞), J. Appl. Probab. 10 (1973), pp. 109-121.
• [8] A. V. Skorohod, Limit theorems for stochastic processes, Theory Probab. Appl. 1 (1956), pp. 261-290. .
• [9] W. Whitt, Some useful functions for functional limit theorems, Math. Oper. Res. 5 (1980), pp. 67-85.