Martin P. W. Zerner

Weak separation properties for self-similar sets

We develop a theory for self-similar sets in Rs that fulfil the weak separation property of Lau and Ngai, which is weaker than the open set condition of Hutchinson.

Velocity and Lyapounov exponents of some random walks in random environment

Abstract We express the asymptotic velocity of random walks in random environment satisfying Kalikows condition in terms of the Lyapounov exponents which have previously been used in the context of large deviations.

Recurrence and transience of contractive autoregressive processes and related Markov chains

We characterize recurrence and transience of nonnegative multivariate autoregressive processes of order one with random contractive coefficient matrix, of subcritical multitype Galton-Watson branching processes in random environment with immigration, and of the related max-autoregressive processes and general random exchange processes. Our criterion is given in terms of the maximal Lyapunov exponent of the coefficient matrix and the cumulative distribution function of the innovation/immigration component.