  In the field of Life Sciences it it very common to deal with extremely
complex systems, from both analytical and computational points of view, due to
the unavoidable coupling of different interacting structures. As an example,
angiogenesis has revealed to be an highly complex, and extremely interesting
biomedical problem, due to the strong coupling between the kinetic parameters
of the relevant branching - growth - anastomosis stochastic processes of the
capillary network, at the microscale, and the family of interacting underlying
biochemical fields, at the macroscale. In this paper an original revisited
conceptual stochastic model of tumor driven angiogenesis has been proposed, for
which it has been shown that it is possible to reduce complexity by taking
advantage of the intrinsic multiscale structure of the system; one may keep the
stochasticity of the dynamics of the vessel tips at their natural microscale,
whereas the dynamics of the underlying fields is given by a deterministic mean
field approximation obtained by an averaging at a suitable mesoscale. While in
previous papers only an heuristic justification of this approach had been
offered, in this paper a rigorous proof is given of the so called "propagation
of chaos", which leads to a mean field approximation of the stochastic relevant
measures associated with the vessel dynamics, and consequently of the
underlying TAF field. As a side though important result, the non-extinction of
the random process of tips has been proven during any finite time interval.
