Stability of precise Laplace's method under approximations ; applications
ESAIM: Probability and Statistics, Tome 3 (1999), pp. 67-88. 
@article{PS_1999__3__67_0,
     author = {Guionnet, Alice},
     title = {Stability of precise {Laplace's} method under approximations ; applications},
     journal = {ESAIM: Probability and Statistics},
     pages = {67--88},
     publisher = {EDP-Sciences},
     volume = {3},
     year = {1999},
     mrnumber = {1716132},
     zbl = {0932.60031},
     language = {en},
     url = {http://www.numdam.org/item/PS_1999__3__67_0/}
}
TY  - JOUR
AU  - Guionnet, Alice
TI  - Stability of precise Laplace's method under approximations ; applications
JO  - ESAIM: Probability and Statistics
PY  - 1999
SP  - 67
EP  - 88
VL  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/PS_1999__3__67_0/
LA  - en
ID  - PS_1999__3__67_0
ER  - 
%0 Journal Article
%A Guionnet, Alice
%T Stability of precise Laplace's method under approximations ; applications
%J ESAIM: Probability and Statistics
%D 1999
%P 67-88
%V 3
%I EDP-Sciences
%U http://www.numdam.org/item/PS_1999__3__67_0/
%G en
%F PS_1999__3__67_0
Guionnet, Alice. Stability of precise Laplace's method under approximations ; applications. ESAIM: Probability and Statistics, Tome 3 (1999), pp. 67-88. http://www.numdam.org/item/PS_1999__3__67_0/

[1] M.A. Arcones and E. Gine, Limit Theorems for U-processes. Ann. Probab. 21 ( 1993) 1494-1542. | MR | Zbl

[2] M.A. Arcones and E. Gine, On the bootstrap of U and V statistics. Ann. Stat. 20 ( 1992) 655-674. | MR | Zbl

[3] G. Ben Arous and M. Brunaud, Méthode de Laplace : Étude variationnelle des fluctuations de diffusions de type "champ moyen". Stochastics 31-32 ( 1990) 79-144. | MR | Zbl

[4] M.Sh. Birman, A proof of the Fredholm trace formula as an application of a simple embedding for kernels of integral operators of trace class in L2(ℝm). Lith-Mat-R-89-30 ( 1989).

[5] E. Bolthausen, Laplace approximation for sums of independent random vectors I. Prob. Th. Rel. Fields 72 ( 1986) 305-318. | MR | Zbl

[6] C. Borell, On the integrability of Banach space valued Walsh polynomials. Séminaire de probabilités XIII. Lecture Notes in Math. 721 ( 1979) 1-3. | EuDML | Numdam | MR | Zbl

[7] D.A. Dawson, Critical dynamics and fluctuations for a mean field model of cooperative behavior. J. Stat. Phys. 31 ( 1983) 247-308. | MR

[8] A. De Acosta and E. Gine, Convergence of moments and related Functionals in the central limit Theorem in Banach spaces. Z. Wahrsch. Verw. Gebiete 48 ( 1979) 213-231. | MR | Zbl

[9] A. Dembo and O. Zeitouni, Large deviations techniques and Applications. Jones and Bartlett ( 1992). | MR | Zbl

[10] J.D. Deuschel and D.W. Stroock, Large deviations. Academic press ( 1989). | MR | Zbl

[11] M. Hitsuda and H. Tanaka, Central limit Theorem for a simple diffusion model for interacting particles. Hiroshima Math. J. 11 ( 1981) 415-423. | MR | Zbl

[12] S. Kusuoka and Y. Tamura, Gibbs measures for mean field potentials. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 ( 1984). | MR | Zbl

[13] H.P. Mac Kean, Fluctuations in the kinetic theory of gases. Comm. Pure Appl. Math. 28 ( 1975) 435-455. | MR

[14] K.R. Parthasarathy, Probability measures on Metric Spaces. Academic Press Inc., New York ( 1968). | MR | Zbl

[15] V.H. De La Pena, Decoupling and Khintchine's inequalities for U-statistics. Ann. Probab. 20 ( 1992) 1877-1892. | MR | Zbl

[16] W. Rudin, Real and complex analysis, second edition, Springer. | MR | Zbl

[17] T. Shiga and H. Tanaka, Central limit Theorem for a System of markovian particles with mean field interaction. Z. Wahrsch. Verw. Gebiete 69 ( 1985) 439-459. | MR | Zbl

[18] B. Simon, Trace ideals and their applications. London Mathematical Society Lecture Notes series 35, Cambridge University press ( 1977). | MR | Zbl

[19] A.-S. Sznitman, Non linear reflecting diffusion process and the propagation of chaos and fluctuations associated. | Zbl

[20] H. Tanaka, Limit Theorems for certain diffusion processes, in Proc. of the Taniguchi Symp, Katata ( 1982) 469-488, Tokyo, Kinokuniya ( 1984). J. Funct. Anal. 56 1984) 311-336. | MR | Zbl