Penalizations of the Brownian motion with a functional of its local times

In this article, we study the family of probability measures (indexed by t ∈ R + ∗ ), obtained by penalization of the Brownian motion with a given functional of its local times at time t . ve that this family tends to a limit measure when t goes to infinity if the functional satisfies some conditions of domination, and we check these conditions in several particular cases.