Invariance principles for random walks in cones

Abstract: We prove invariance principles for a mulditimensional random walk conditioned to stay in a cone. Our first result concerns convergence towards the Brownian meander in the cone. Furthermore, we prove functional convergence of $h$-transformed random walk to the corresponding $h$-transform of the Brownian motion. Finally, we prove an invariance principle for bridges of a random walk in a cone.