Biased random walks on infinite trees

In the present thesis we consider random walks on different types of infinite trees which have a distinguished direction, a bias. This attracts the moving particle to a certain extent. We are interested in how fast the particle escapes from its starting point. For different types of trees we thus calculate the asymptotic rate of escape, the speed of the random walk, as a function of the bias parameter. We develop a method which needs two prerequisites: The connections between random walks and electric networks. The observation of the random walk in the space of directed rooted unlabeled trees. The latter enables us to treat the non-stationary transient random walk by means of stationary stochastic processes, especially ergodic theory.