A Functional Limit Theorem for Lattice Oscillating Random Walks

This paper is devoted to an invariance principle for Kemperman's model of oscillating random walk on Z. This result appears as an extension of the invariance principal theorem for classical random walks on Z or reflected random walks on N-0. Relying on some natural Markov sub-process which takes into account the oscillation of the random walks between Z(-) and Z(+), we first construct an aperiodic sequence of renewal operators acting on a suitable Banach space and then apply a powerful theorem proved by S. Gouezel.