  Angiogenesis is a multiscale process by which a primary blood vessel issues
secondary vessel sprouts that reach regions lacking oxygen. Angiogenesis can be
a natural process of organ growth and development or a pathological induced by
a cancerous tumor. A mean field approximation for a stochastic model of
angiogenesis consists of partial differential equation (PDE) for the density of
active tip vessels. Addition of Gaussian and jump noise terms to this equation
produces a stochastic PDE that defines an infinite dimensional L\'evy process
and is the basis of a statistical theory of angiogenesis. The associated
functional equation has been solved and the invariant measure obtained. The
results are compared to a direct numerical simulation of the stochastic model
of angiogenesis and invariant measure multiplied by an exponentially decaying
factor. The results of this theory are compared to direct numerical simulations
of the underlying angiogenesis model. The invariant measure and the moments are
functions of the Korteweg-de Vries soliton which approximates the deterministic
density of active vessel tips.
