【作者】 孙利荣；

【导师】 耿显民；

【作者基本信息】 南京航空航天大学 ， 计算数学， 2002， 硕士

【摘要】 本文研究了时滞为1的动态投入产出模型的稳定增长解的存在问题。 动态投入产出模型最早由W·Leontief提出，因其稳定解问题没有解决，使它的应用十分有限，华罗庚研究了关于时间齐次的投入产出模型，得到了稳定解。本文对在上述基础上构造的一类时滞为1的动态投入产出模型，进行了深入研究，将随机因素逐步考虑进去，即对投入产出消耗系数矩阵为随机的情况(投资系数矩阵为随机的情况与投入产出消耗系数矩阵为随机的情况大致相同，这里就不再证明)，以及二者同时为随机矩阵时所得到的动态投入产出模型的稳定增长解问题，利用现代概率分析及马氏过程的工具，证明了不存在随机动态投入产出模型的稳定增长解；即投入产出模型反映的经济系统必须经常进行调整，其崩溃时间为无穷大的概率为零。更多还原

【Abstract】 This paper researches the existent problem of the stable increase solution for one dynamic input-output model that the time lag is one.Leontief first gives out the dynamic input-output model, but he don’t solve its stable increase solution, which makes its application limited. Hua-luogeng researches the homogeneous input-output model, and gets the stable solution. This paper is mainly the dynamic input-output model that the time lag is one, which is base on the above models. After studying, we consider stochastic factor step by step in it, namely when consumption coefficient matrix is stochastic (when investment matrix is stochastic, it is almost same. So we don’t research it), and they are both stochastic, then we research the stable increase solution. We utilize the means of the modern stochastic analysis and Markov process, that the stochastic dynamic input-output model don not exist the stable solution is proved. Namely, economic system must is adjusted constantly. The probability that the collapse time of the economic system is o is one.更多还原