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Abstrakty
We prove a large deviations principle (LDP) for partial sums U-processes indexed by the half line. The LDP can be formulated on a suitable subset of the set of all absolutely continuous paths. We endow the space with a topology, which is stronger than the usual topology of uniform convergence on compact intervals. An LDP for the maximum of the sample path of the U-processes is obtained as a particular application.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
1--13
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Fakultät für Mathematik, Universität Bielefeld, Postfach 10-0131, D-33501 Bielefeld, Germany
Bibliografia
- [1] M. A. Arcones and E. Giné, U-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of U-statistics with estimated parameters, Stochastic Process. Appl. 52 (1994), pp. 17-38.
- [2] A. A. Borovkov, Boundary-value problems for random walks and large deviations in function spaces, Theory Probab. Appl. 12 (1967), pp. 575-595.
- [3] A. Dembo and T. Zajic, Large deviations: From empirical mean and measure to partial sums process, Stochastic Process. Appl. 57 (1995), pp. 191-224.
- [4] A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Springer, New York 1998.
- [5] R. L. Dobrushin and E. A. Pechersky, Large deviations for tandem queueing systems, J. Appl. Math. Stochastic Anal. 7 (1994), pp. 301-330.
- [6] - Large deviations for random processes with independent increments on infinite intervals, preprint, 1995.
- [7] M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time. III, Comm. Pure Appl. Math. 29 (1976), pp. 389-461.
- [8] N. G. Duffield and N. O'Connell, Large deviations and overflow probabilities for the general single-server queue, with applicalions, Math. Proc. Cambridge Philos. Soc. 118 (1995), pp. 363-374.
- [9] P. Eichelsbacher, Large deviations for products of empirical probability measures in the τ-topology, J. Theoret. Probab. 10, No. 4 (1997), pp. 903-920.
- [10] - Partial sums U-processes large deviations in stronger topologies, Statist. Probab. Lett. 38 (1998), pp. 207-214.
- [11] - and M. Löwe, Large deviations for partial sums U-processes, Theory Probab. Appl. 43 (1998), pp. 97-115.
- [12] W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc. 58 (1963), pp. 13-30.
- [13] A. A. Mogulskii, Large deviations for trajectories of multidimensional random walks, Theory Probab. Appl. 21 (1976), pp. 300-315.
- [14] N. O'Connell, A large deviations principle with queueing applications, preprint, 1997.
- [15] S. R. S. Varadhan, Asymptotic probabilities and differential equations, Comm. Pure Appl. Math. 19 (1966), pp. 261-286.
Typ dokumentu
Bibliografia
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