This paper considers a neoclassical optimal growth problem where the shock that perturbs the economy in each time period is potentially unbounded on the state space. Sufficient conditions for existence, uniqueness and stability of equilibria are derived in terms of the primitives of the model...

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...

New results in the asymptotic theory of Markov processes are applied to analysis of the long-run behaviour exhibited by optimal growth models with unbounded productivity shock. The techniques developed here are geometrically intuitive, and are shown to imply global stability for a popular model...

This note studies conditions under which sequences of capital per head generated by stochastic optimal accumulation models have law of large numbers and central limit properties. The regularity condition used on the productivity shock is somewhat different to that of previous studies. In...

The paper introduces a multiplicative drift condition for evaluating stochastic economic models. The drift condition is shown to permit computation of quantitative bounds for extreme event probabilities in terms of the model primitives. By way of illustration, the technique is applied to a...

The paper gives conditions under which stationary distributions of Markov models depend continuously on the parameters. It extends a well-known parametric continuity theorem for compact state space to the unbounded setting of standard econometrics and time series analysis. Applications to...

We consider discrete time Markov chains on general state space. It is shown that a certain property referred to here as nondecomposability is equivalent to irreducibility, and that a Markov chain with invariant distribution is irreducible if and only if the invariant distribution is unique and...

The standard one-sector stochastic optimal growth model is shown to be not just ergodic but geometrically ergodic. In addition, it is proved that the time series generated by the optimal path satisfy the Law of Large Numbers and the Central Limit Theorem.

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The paper considers random economic systems generating nonlinear time series on the positive half-ray R+. Using Liapunov techniques, new conditions for existence, uniqueness and stability of stationary equilibria are obtained. The conditions generalize earlier results from the mathematical...