Sharp estimates of deviations of the sample mean in many dimensions

 Access to full text

 Full (PDF)

1. [1] R. Azencott, Petites perturbations aléatoires des systèmes dynamiques: développements asymptotiques, Bull. Sci. Math. (2ème série), Vol. 109, 1985, pp. 253-308. Zbl0591.60023MR822827
2. [2] R.R. Bahadur and Rao, On deviations of the sample mean, Ann. Math. Statist., Vol. 31, 1960, pp. 1015-1027. Zbl0101.12603MR117775
3. [3] P. Baldi, On the exact equivalent of the exit time of a Brownian motion from an open set, Prépublication Laboratoire de Probabilités, Université Paris6, 1991, 71-91. 
4. [4] P. Baldi, Exact asymptotics for the probability of exit from a domain and applications to simulation, Ann. Probab., Vol. 23, 1995, pp. 1644-1670. Zbl0856.60033MR1379162
5. [5] C. Bellaïche, Comportement asymptotyque de p(t,, x, y) quand t → 0 (points éloignés). In: Gódesiques et diffusions en temps petit, Astérisque, Vol. 84-85, 1981, pp. 151-187. Zbl0507.60074
6. [6] N. Bleistein and R.A. Handelsman, Asymptotic expansion of integrals, Dover, New York. Zbl0327.41027MR863284
7. [7] A.A. Borovkov and B.A. Rogozin, On the multidimensional central limit theorem, Th. Probab. Appl., Vol. 10, 1965, pp. 55-62. Zbl0139.35206MR173279
8. [8] R.S. Ellis, Entropy Large Deviations and Statistical Mechanics, Springer Verlag, New York, Berlin, Heidelberg, Tokyo. Zbl0566.60097MR793553
9. [9] N.J. Hickso, Notes On Differential Geometry, Van Nostrand Math. Studies3, 1965. Zbl0132.15104MR179691
10. [10] M. Iltis, Sharp Asymptotics of Large Deviations in Rd, J. Theor. Probab., Vol. 8, 1995, pp. 501-522. Zbl0831.60042MR1340824
11. [11] P. Ney, Dominating points and the asymptotics of large deviations for random walk on Rd, Ann. Probab., Vol. 11, 1983, pp. 158-167. Zbl0503.60035MR682806
12. [12] W.D. Richter, Laplace-Gauß Integrals, Gaussian Measure Asymptotic Behaviour and Probability of moderate Deviations, Z. Anal. ihre Anwendugen, Vol. 4, 1985, pp. 257- 267. Zbl0572.60035MR807135
13. [13] T.R. Rockafellar, Convex Analysis, Princeton University Press, Princeton N.J., 1970. Zbl0193.18401MR274683

1. Pierre Pudlo, Large deviations and full Edgeworth expansions for finite Markov chains with applications to the analysis of genomic sequences