带有能源的随机动态柯布-道格拉斯生产函数

在考虑能源作为投入要素和经济环境随机动态变化的情况下，将经典的柯布-道格拉斯生产函数推广到随机动态的形式.首先给出了随机动态C -D生产函数的随机微分方程形式,证明了该生产函数解的存在性和唯一性；其次，进一步分析了解的Markov性质和扩散性质,并分别利用漂移系数和扩散系数给出了产出弹性的计算公式.最后，还给出了经济增长中资本、劳动与能源协调发展的必要条件，并通过实例验证了模型的有效性.

The Stochastic Dynamic Cobb -Douglas Production Function with the Input of Energy

Considering the energy be one input factor and the economic environment be stochastic and dynamically changing, the classic Cobb -Douglas production function was extended to the stochastic and dynamic case. Firstly, the different equation of the stochastic and dynamic C -D production function was expressed, and the existence and unique of the solution of the production function were proved. Secondly, the character of Markov and diffusion of the solution were analyzed. Furthermore, the formulas of flexibility of the output were given by using the excursion coefficient and diffusion coefficient. Finally, a necessary condition of capital, labor and energy coordinately developing in the economic growth was given, and some examples were given to demonstrate the validity of the model proposed.