  Through this paper we analyze the ergodic properties of continuous time
Markov chains with values on the one-dimensional spin lattice 1,...,d}^N (also
known as the Bernoulli space). Initially, we consider as the infinitesimal
generator the operator $L={\mc L}_A -I$, where \mc L_A is a discrete time
Ruelle operator (transfer operator), and A:{1,...,d}^N \to R is a given fixed
Lipschitz function. The associated continuous time stationary Markov chain will
define the\emph{a priori}probability.
  Given a Lipschitz interaction V:\{1,...,d\}^{\bb N}\to \mathbb{R}, we are
interested in Gibbs (equilibrium) state for such $V$. This will be another
continuous time stationary Markov chain. In order to analyze this problem we
will use a continuous time Ruelle operator (transfer operator) naturally
associated to V. Among other things we will show that a continuous time
Perron-Frobenius Theorem is true in the case V is a Lipschitz function.
  We also introduce an entropy, which is negative, and we consider a
variational principle of pressure. Finally, we analyze large deviations
properties for the empirical measure in the continuous time setting using
results by Y. Kifer.
