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We describe scaling limits of recurrent excited random walks (ERWs) on integers in i.i.d. cookie environments with a bounded number of cookies per site. We allow both positive and negative excitations. It is known that ERW is recurrent if and only if the expected total drift per site, delta, belongs to the interval [-1,1]. We show that if |delta, 12 pages

Soit ξ(k, n) le temps local d'une marche aleatoire simple et symetrique sur la droite reelle. Nous donnons une approximation forte de la difference des temps locaux ξ(k, n) ― ξ(0, n) en termes d'un drap Brownien et d'un processus de Wiener independant, evalue au temps local d'un mouvement Brownien independant. Des applications de ce resultat sont etablies.

We discuss the convergence of the expected times until the partial sums of a sequence of independent, identically distributed random variables with zero means and unit variances first rise a height $h$ above their previous minimum as $h \rightarrow \infty$. We also consider the convergence as $r \rightarrow \infty$ of the expected times until the range of these partial sums exceeds a value $r$. Applications of these results to a quality control procedure and to queueing theory are mentioned.