We consider non-conservative positive semigroups and obtain necessary sufficient conditions for uniform exponential contraction in weighted total variation norm. This ensures the existence of Perron eigenelements provides quantitative estimates spectral gap, complementing Krein–Rutman theorems generalizing probabilistic approaches. The proof is based on a non-homogenous h $h$ -transform semigro...

In this paper linear hyperbolic cocycles are classiied by the relation of topological conjugacy. Roughly speaking, two linear cocycles are conjugate if there exists a homeomorphism which maps their tra-jectories into each other. The problem of classiication of discrete-time deterministic hyperbolic dynamical systems was investigated by Rob-bin (1972). He proved that there exist 4d classes of d-...

A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...