We study surface growth models exhibiting anomalous scaling of the local surface fluctuations. An analytical approach to determine the local scaling exponents of continuum growth models is proposed. The method allows one to predict when a particular growth model will have anomalous properties ( $\alpha \ne {\alpha }_{\mathrm{loc}}$) and to calculate the local exponents. Several continuum growth equations are examined as examples.

• Received 27 July 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.4594