Large deviations estimates for some white noise distributions (original) (raw)

We consider a positive distribution Φ which defines a probability measure µ = µ Φ on X ′ the dual of some real nuclear Fréchet space. We consider the family {µǫ, ǫ > 0}, where µǫ denotes the image measure of µ by the measurable map gǫ on X ′ given by gǫ(λ) = a(ǫ)λ, λ ∈ X ′ , where a is real positive valued function on R such that lim ǫ→0 a(ǫ) = 0. A large deviation principle is proved for the family {µǫ, ǫ > 0}, and application to stochastic differential equations is given. . Amir Dembo and Ofer Zeitouni, in their book emphasize applications related to electrical engineering. Cramér in [13] proved Cramér's theorem for distribution µ on R which is not singular to the Lebesgue measure. On the other hand, white noise analysis provides a lot of powerful tools as well for infinite dimensional calculus as for probability theory, a quite complete overview is given by [21] and . So, the combination of these two subjects should inspire new results and give a feed-back to each of them.