no. 3
Sharp estimates of deviations of the sample mean in many dimensions
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 3, pp. 371-385 
@article{AIHPB_1997__33_3_371_0,
     author = {Andriani, Cristina and Baldi, Paolo},
     title = {Sharp estimates of deviations of the sample mean in many dimensions},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {371--385},
     year = {1997},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {3},
     mrnumber = {1457057},
     zbl = {0882.60022},
     language = {en},
     url = {https://www.numdam.org/item/AIHPB_1997__33_3_371_0/}
}
TY  - JOUR
AU  - Andriani, Cristina
AU  - Baldi, Paolo
TI  - Sharp estimates of deviations of the sample mean in many dimensions
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1997
SP  - 371
EP  - 385
VL  - 33
IS  - 3
PB  - Gauthier-Villars
UR  - https://www.numdam.org/item/AIHPB_1997__33_3_371_0/
LA  - en
ID  - AIHPB_1997__33_3_371_0
ER  - 
%0 Journal Article
%A Andriani, Cristina
%A Baldi, Paolo
%T Sharp estimates of deviations of the sample mean in many dimensions
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1997
%P 371-385
%V 33
%N 3
%I Gauthier-Villars
%U https://www.numdam.org/item/AIHPB_1997__33_3_371_0/
%G en
%F AIHPB_1997__33_3_371_0
Andriani, Cristina; Baldi, Paolo. Sharp estimates of deviations of the sample mean in many dimensions. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 3, pp. 371-385. https://www.numdam.org/item/AIHPB_1997__33_3_371_0/

[1] R. Azencott, Petites perturbations aléatoires des systèmes dynamiques: développements asymptotiques, Bull. Sci. Math. (2ème série), Vol. 109, 1985, pp. 253-308. | Zbl | MR

[2] R.R. Bahadur and Rao, On deviations of the sample mean, Ann. Math. Statist., Vol. 31, 1960, pp. 1015-1027. | Zbl | MR

[3] P. Baldi, On the exact equivalent of the exit time of a Brownian motion from an open set, Prépublication Laboratoire de Probabilités, Université Paris 6, 1991, 71-91.

[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. | Zbl | MR

[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. | Zbl

[6] N. Bleistein and R.A. Handelsman, Asymptotic expansion of integrals, Dover, New York. | MR

[7] A.A. Borovkov and B.A. Rogozin, On the multidimensional central limit theorem, Th. Probab. Appl., Vol. 10, 1965, pp. 55-62. | Zbl | MR

[8] R.S. Ellis, Entropy Large Deviations and Statistical Mechanics, Springer Verlag, New York, Berlin, Heidelberg, Tokyo. | Zbl | MR

[9] N.J. Hickso, Notes On Differential Geometry, Van Nostrand Math. Studies 3, 1965. | Zbl | MR

[10] M. Iltis, Sharp Asymptotics of Large Deviations in Rd, J. Theor. Probab., Vol. 8, 1995, pp. 501-522. | Zbl | MR

[11] P. Ney, Dominating points and the asymptotics of large deviations for random walk on Rd, Ann. Probab., Vol. 11, 1983, pp. 158-167. | Zbl | MR

[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. | Zbl | MR

[13] T.R. Rockafellar, Convex Analysis, Princeton University Press, Princeton N.J., 1970. | Zbl | MR