Geodesic
Large Deviations for Gaussian Stochastic Processes with Sample Paths in Orlicz Spaces
Canadian journal of mathematics, Tome 40 (1988) no. 2, pp. 487-501

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a complete, separable metric space, and a family of probability measures on the Borel subsets of X. We say that obeys the large deviation principle (LDP) with a rate function I( · ) if there exists a function I( · ) from X into [0, ∞] satisfying: (i) 0 ≦ I(x) ≦ ∞ for all x ∊ X, (ii) I( · ) is lower semicontinuous, (iii) for each 1 < ∞ the set {x:I(x) ≦ 1} is compact set in X, (iv) for each closed set C ⊂ X (v) for each open set U ⊂ X It is easy to see that if A is a Borel set such that then where A 0 and Ā are respectively the interior and the closure of the Borel set A. 
Large Deviations for Gaussian Stochastic Processes with Sample Paths in Orlicz Spaces. Canadian journal of mathematics, Tome 40 (1988) no. 2, pp. 487-501. doi: 10.4153/CJM-1988-020-0
@misc{10_4153_CJM_1988_020_0,
     title = {Large {Deviations} for {Gaussian} {Stochastic} {Processes} with {Sample} {Paths} in {Orlicz} {Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {487--501},
     year = {1988},
     volume = {40},
     number = {2},
     doi = {10.4153/CJM-1988-020-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-020-0/}
}
TY  - JOUR
TI  - Large Deviations for Gaussian Stochastic Processes with Sample Paths in Orlicz Spaces
JO  - Canadian journal of mathematics
PY  - 1988
SP  - 487
EP  - 501
VL  - 40
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-020-0/
DO  - 10.4153/CJM-1988-020-0
ID  - 10_4153_CJM_1988_020_0
ER  - 
%0 Journal Article
%T Large Deviations for Gaussian Stochastic Processes with Sample Paths in Orlicz Spaces
%J Canadian journal of mathematics
%D 1988
%P 487-501
%V 40
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-020-0/
%R 10.4153/CJM-1988-020-0
%F 10_4153_CJM_1988_020_0

[1] 1. Bahadur, R. R. and Zabell, S. L., Large deviations of the sample mean in general vector spaces, Ann. Probab. 7 (1979), 587–621. Google Scholar

[2] 2. Byczkowski, T., Gaussian measures on L spaces, 0 &lt; p &lt; ∞, Studia Math. 59 (1977), 249–261. Google Scholar

[3] 3. Byczkowski, T., Norm convergent expansion for L-valued Gaussian random elements, Studia Math. 64 (1979), 87–95. Google Scholar

[4] 4. Byczkowski, T. and Zak, T., On the integrability of Gaussian random vectors, Lecture Notes in Math. 828 (Springer, New York, 1979), 21–30. Google Scholar

[5] 5. Cramer, H., Sur un nouveau théorème-limite de la théorie des probabilités, Actualités Sci. Indust. 736 (1938), 5–23. Google Scholar

[6] 6. Donsker, M. D. and Varadhan, S. R. S., Asymptotic evaluation for certain Markov processes expectations for large-time III, Comm. Pure Appl. Math. 29 (1976), 389–461. Google Scholar

[7] 7. Kallianapur, G. and Oodaira, H., Freidlin-Wentzell type estimates for abstract Wiener spaces, Sankhya 40, Series A (1978), 116–137. Google Scholar

[8] 8. Lawniczak, A. T., Gaussian measures on Orlicz spaces and abstract Wiener spaces, Lecture Notes in Math. 939 (Springer, New York, (1982), 81–97. Google Scholar

[9] 9. Lawniczak, A. T., High level occupation times for Gaussian stochastic processes with sample paths in Orlicz spaces, Can. J. Math. 39 (1987), 239–256. Google Scholar

[10] 10. Marlow, N., High level occupation times for continuous Gaussian processes, Ann. Probab. 3 (1973), 388–397. Google Scholar

[11] 11. Rolewicz, S., Metric linear spaces (Polish Scientific Publishers, PWN, 1972). Google Scholar

[12] 12. Stroock, D. W., An introduction to the theory of large deviations (Springer-Verlag, New York, (1984). Google Scholar | DOI

[13] 13. Varadhan, S. R. S. Large deviations and applications, SIAM (1984). Google Scholar | DOI

Cité par Sources :