Uniform moderate deviations of functional empirical processes of Markov chains

• Autorzy: Guillin A.
• Języki publikacji: EN

Abstrakty

EN

We obtain uniform (in time) moderate deviations for the functional empirical process of a general state space Markov chain under the geometric ergodicity assumption, and a regularity condition for the initial measure, by the regeneration split chain method. Our results deal both with bounded and unbounded class of functions.

Słowa kluczowe

EN

moderate deviations; Markov chains; geometric ergodicity; regeneration split chain method; functional empirical process

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 2
• Strony: 237--260
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Guillin A.

• Université Clermont Auvergne, Clermont-Ferrand, France

Bibliografia

• [1] J,-D. Deuschel and D. W. Stroock, Large Deviations, Academic Press, Boston 1989.
• [2] P. Dupuis and R. S. Ellis, A Weak Convergence Approach to the Theory of Large Deviations, Wiley, Chichester 1997.
• [3] I. A. Ibrahimov and R. Z. Khasminskii, Asymplotic Estimation Theory (in Russian), Nauka, Moscow 1979.
• [4] J.-Y. Jaffray, On the maximum of conditional entropy for upper/lower probabilities generated by random sets, in: Random Sets: Theory and Applications, J. Goutsias, R. P. S. Mahler and H. T. Nguyen (Eds.), The IMA Volumes in Mathematics and its Applications, Springer, New York 1997, pp. 105-127.
• [5] G. Matheron, Random Sets and Integral Geometry, Wiley, New York 1975.
• [6] A. Meyerowitz, F. Richman and E. Walker, Calculating maximum-entropy probability densities for belief functions, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 2, No. 4 (1994), pp. 377-389.
• [7] I. S. Molchanov, Limit Theorems for Unions of Random Closed Sets, Lecture Notes in Math. 1561, Springer, Berlin 1993.
• [8] T. Norberg, An ordered random set coupling, Probab. Theory Related Fields 37 (1992) pp. 161-163.
• [9] T. Norberg, On the existence of ordered couplings of random sets - with applications, Israel J. Math. 77 (1992), pp. 241-264.
• [10] R. Schneider, Convex bodies: the Brunn-Minkowski theory, Encyclopaedia Mith. Appl. 44, Cambridge University Press, 1993.
• [11] A. W. van der Vaart and J. A. Wellner, Weak Convergence and Empirical Processes withApplications to Statistics, Springer, New York 1996.