  We develop a stochastic approach for describing 3D-phase transformations
ruled by time-dependent correlated nucleation at solid surfaces. The kinetics
is expressed as a series of correlation functions and, at odds with modeling
based on Poisson statistics, it is formulated in terms of actual nucleation
rate. It is shown that truncation of the series up to second order terms in
correlation functions provides a very good approximation of the kinetics. The
time evolution of both total amount of growing phase and surface coverage by
the new phase have been determined. The theory is applied to describe
progressive nucleation with parabolic growth under time dependent hard-disk
correlation. This approach is particularly suitable for describing
electrochemical deposition by nucleation and growth where correlation effects
are significant. In this ambit the effect of correlated nucleation on the
behavior of kinetic quantities used to study electrodeposition has also been
investigated.
