ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60J10 Chiang, Tzuu-Shuh, Sheu, Shenn-Jyi, Academia Sinica, Taipei, Taiwan. Large Deviation of Small diffusions in discontinuous media For a diffusion process, dX(t) = b(X(t))dt+ϵσ(X(t))dW (t), we consider the large deviation of P^{ϵ}(∥X(.)−ϕ(.)∥ < δ, ∥u(.)−ψ(.)∥ < δ, ∥ℓ(.)−η(.)∥) < δ). Here, ϕ(t) is the occupation time of X(t) in the positive half space and ℓ(t) is the local time of X(t) at 0. The drift and diffusion coefficients are assumed smooth except possibly along the hyperplane in d-dimensional space where the first coordinate is 0. The exact formula of the rate function is also given.