Tightness and exponential tightness of Gaussian probabilities
ESAIM: Probability and Statistics, Tome 24 (2020), pp. 113-126.

We prove a simple criterion of exponential tightness for sequences of Gaussian r.v.’s with values in a separable Banach space from which we deduce a general result of Large Deviations which allows easily to obtain LD estimates in various situations.

Reçu le :
Accepté le :
Première publication :
Publié le :
DOI : 10.1051/ps/2020003
Classification : 60F10, 60B12
Mots-clés : Gaussian probabilities, large deviations 
@article{PS_2020__24_1_113_0,
     author = {Baldi, Paolo},
     title = {Tightness and exponential tightness of {Gaussian} probabilities},
     journal = {ESAIM: Probability and Statistics},
     pages = {113--126},
     publisher = {EDP-Sciences},
     volume = {24},
     year = {2020},
     doi = {10.1051/ps/2020003},
     mrnumber = {4071318},
     zbl = {1434.60082},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ps/2020003/}
}
TY  - JOUR
AU  - Baldi, Paolo
TI  - Tightness and exponential tightness of Gaussian probabilities
JO  - ESAIM: Probability and Statistics
PY  - 2020
SP  - 113
EP  - 126
VL  - 24
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ps/2020003/
DO  - 10.1051/ps/2020003
LA  - en
ID  - PS_2020__24_1_113_0
ER  - 
%0 Journal Article
%A Baldi, Paolo
%T Tightness and exponential tightness of Gaussian probabilities
%J ESAIM: Probability and Statistics
%D 2020
%P 113-126
%V 24
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ps/2020003/
%R 10.1051/ps/2020003
%G en
%F PS_2020__24_1_113_0
Baldi, Paolo. Tightness and exponential tightness of Gaussian probabilities. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 113-126. doi : 10.1051/ps/2020003. http://archive.numdam.org/articles/10.1051/ps/2020003/

[1] R. Azencott, Grandes déviations et applications, Eighth Saint Flour Probability Summer School – 1978, Saint Flour, 1978. Vol. 774 of Lecture Notes in Math. Springer, Berlin (1980), 1–176. | MR | Zbl

[2] P. Baldi, Large deviations and stochastic homogenization. Ann. Mat. Pura Appl. 151 (1988) 161–177. | MR | Zbl

[3] P. Billingsley, Convergence of probability measures. John Wiley & Sons, Inc., New York-London-Sydney (1968). | MR | Zbl

[4] A. De Acosta Upper bounds for large deviations of dependent random vectors. Z. Wahrsch. Verw. Gebiete 69 (1985) 551–565. | MR | Zbl

[5] L. Decreusefond and A. S. Üstünel, Stochastic analysis of the fractional Brownian motion. Potential Anal. 10 (1999) 177–214. | MR | Zbl

[6] A. Dembo and O. Zeitouni, Large deviations techniques and applications. Vol. 38 of Stochastic Modelling and Applied Probability. Springer-Verlag, Berlin (2010). | MR | Zbl

[7] J.-D. Deuschel and D.W. Stroock, Large deviations. Vol. 137 of Pure and Applied Mathematics. Academic Press, Inc., Boston, MA (1989). | MR | Zbl

[8] M.D. Donsker and S.R.S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time. III. Commun. Pure Appl. Math. 29 (1976) 389–461. | MR | Zbl

[9] R.S. Ellis, Large deviations for a general class of random vectors. Ann. Probab. 12 (1984) 1–12. | MR | Zbl

[10] X Fernique, Intégrabilité des vecteurs gaussiens. C. R. Acad. Sci. Paris Sér. A-B 270 (1970) A1698–A1699. | MR | Zbl

[11] X. Fernique, Regularité des trajectoires des fonctions aléatoires gaussiennes. École d’Été de Probabilités de Saint-Flour, IV-1974. Vol. 480 of Lecture Notes in Math. Springer, Berlin (1975) 1–96. | MR | Zbl

[12] J. Gärtner, On large deviations from an invariant measure. Teor. Verojatnost. i Primenen. 22 (1977) 27–42. | MR | Zbl

[13] M. Schilder, Some asymptotic formulas for Wiener integrals. Trans. Am. Math. Soc. 125 (1966) 63–85. | DOI | MR | Zbl

Cité par Sources :

The author acknowledges the MIUR Excellence Department Project awarded to the Dipartimento di Matematica, Università di Roma “Tor Vergata”, CUP E83C18000100006.