Recurrence and transience of multitype branching random walks

We study a discrete time Markov process with particles being able to perfor m discrete time random walks and create new particles, known as branching r andom walk. (BRW). We suppose that there are particles of different types, and the transition probabilities, as well as offspring distribution, depend on the type and the position of the particle. Criteria of (strong) recurre nce and transience are presented, and some applications (spatially homogene ous case, Lamperti BRW, many-dimensional BRW) are studied. (C) 2001 Elsevie r Science B.V. All rights reserved. MSC: 60J10; 60J80.