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Angiogenesis can be a natural process of organ growth and development or a pathological one induced by a cancerous tumor. A mean-field approximation for a stochastic model of angiogenesis consists of a partial differential equation (PDE) for the density of active vessel tips. Addition of Gaussian and jump noise terms to this equation produces a stochastic PDE that defines an infinite-dimensional L\u00e9vy 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 of this theory are compared to direct numerical simulations of the underlying angiogenesis model. 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