Asymptotic Growth under Uncertainty: Existence and Uniqueness
利用反射原理，证明了连续时间不确定性下经典索洛方程解的存在唯一性，适用于严格凹生产函数类，并给出了稳态分布存在的条件。
This paper demonstrates, using the Reflection Principle, the existence and uniqueness of the solution to the classic Solow equation under continuous time uncertainty for the class of strictly concave production functions which are continuously differentiable on the nonnegative real numbers. This class contains all CES functions with elasticity of substitution less than unity. A steady state distribution also exists for this class of production functions which have a bounded slope at the origin. A condition on the drift-variance ratio of the stochastic differential equation alone, independent of technology and the savings ratio, is found to be necessary for the existence of a steady state.