  The universal fractality of river networks is very well known, however
understanding of the underlying mechanisms for them is still lacking in terms
of stochastic processes. By introducing probability changing dynamically, we
have described the fractal natures of river networks stochastically. The
dynamical probability depends on the drainage area at a site that is a key
dynamical quantity of the system, meanwhile the river network is developed by
the probability, which induces dynamical persistency in river flows resulting
in the self-affine property shown in real river basins, although the process is
a Markovian process with short-term memory.
