  We study the algebraic decay of the survival probability in open hierarchical
graphs. We present a model of a persistent random walk on a hierarchical graph
and study the spectral properties of the Frobenius-Perron operator. Using a
perturbative scheme, we derive the exponent of the classical algebraic decay in
terms of two parameters of the model. One parameter defines the geometrical
relation between the length scales on the graph, and the other relates to the
probabilities for the random walker to go from one level of the hierarchy to
another. The scattering resonances of the corresponding hierarchical quantum
graphs are also studied. The width distribution shows the scaling behavior
$P(\Gamma) \sim 1/\Gamma$.
