We investigate stochastic structure in hot-star winds. The structure (i.e. inhomogeneities such as clumps and shocks) is generated by the instability of the line driving mechanism in the inner wind. It is self-excited in the sense that it persists even in the absence of explicit perturbations. The evolution of structure as it moves out with the flow is quantified by the radial dependence of statistical properties such as the clumping factor and the velocity dispersion. We find that structure evolves under the influence of two competing mechanisms. Dense clumps pressure-expand into the rarefied gas that separates them, but this expansion is counteracted by supersonic collisions among the clumps, which tend to compress them further. Because of such ongoing collisions, clumps can survive over an extended region out of pressure equilibrium with the rarefied surrounding gas. Moreover, the line-driving force has little rôle in maintaining the structure beyond about 20-30 R*, implying that the outer evolution can be simplified as a pure gasdynamical problem. In modelling the distant wind structure we find it is necessary to maintain a relatively fine constant grid spacing to resolve the often quite narrow dense clumps. We also find that variations in the heating and cooling, particularly the ``floor’’ temperature to which shock-compressed gas is allowed to cool, can affect both the density and temperature variation. Finally, we find that increasing the value of the line-driving cut-off parameter kappamax can significantly enhance the level of flow structure. Overall, the results of our work suggest that structure initiated in the inner wind acceleration region can survive to substantial distances ( ~100 R*), and thus can have an important influence on observational diagnostics (e.g. infrared and radio emission) formed in the outer wind.