Some Asymptotic Properties of the Continuous-TimeStochastic Solow Model

The paper reconsiders the continuous-time stochastic Solow model and proves that the solution of the stochastic differential equation that characterizes the model is positive under the conditions of Merton's (1975) model, which fills a gap of his result. By the trivial solution's exponential instability of stochastic differential equations and combining with the previous Merton's result, we find the capital/labor ratio will show the steady-state (or asymptotic) distribution or exponential growth. In these results, variances of population growth and capital accomulation play important roles.