A SCHILDER THEOREM FOR NONREGULAR BROWNIA N FUNCTIONALS

Let f: [0, 1] --> R be a alpha-holderian function (with f(0) = 0 and 0 < alpha < 1/2) and psi(f) = \\g-f\\alpha, where \\ \\alpha is a norm equivalent to the usual holderian norm. We prove a Schilder theorem fo r psi(f), i. e. we find an equivalent, as epsilon --> 0, of E (exp - 1 /2epsilon psi(f) (square-root epsilonB) where B is a linear brownian m otion. This equivalent depends, in a qualitative manner, on the ''dist ance'' between f and the origin.