Log-Linearization of Perturbed Dynamical Systems, With Applications to Optimal Growth.

It is common to study the asymptotic properties of log-linear stochastic systems by analyzing the behaviour of their linear counterparts. In this paper a formal justification for analysis by log-linearization is given. As an application, a new existence, uniqueness and stability condition is derived for equilibria in a standard class of multisector growth models with stochastic production. The condition can be seen as a generalization of existing equilibrium conditions for this class of models.