Stochastic Urban Model of Land-use Pattern Formation

首先，在每个居民利润最大化的基本假设下，建立了描述土地利用变化的随机城市模型。该模型表明，整个城市的土地利用变化是一个马尔可夫型随机过程，然后引入表征随机城市模型的量F-函数，阐明了F-函数使城市的土地利用最小地收敛于事实的条件，并在此基础上得到了以下结果：1)土地利用变化过程中存在着一种状态转换在参数的微小差异中发生巨大变化的突变现象，对调控和诱导策略产生重大影响。2)结果表明，城市土地利用率自然分为高、低两个区域，平均土地利用率也存在差异。3)可以证明，土地利用状态的出现概率增加的条件下，土地利用连续性指数是大的，因此，它表明，土地利用连续性自然上升的城市。4)利用随机城市模型分析了地震破坏城市后重建过程中的土地利用变化，以及土地利用格局的混乱，结果表明城市土地利用格局自然恢复到了灾前的状态，并推导了反映两个地点土地利用相关性的空间相关函数的函数形式。理论公式与真实的数据的适用性往往表明了模型参数估计的可能性。最后，为了便于分析，本文对土地利用类型为两种的情况进行了讨论，但将模型扩展到土地利用类型大于两种的情况，说明理论结论是可以推广的。

First, under basic assumption that each inhabitant maximizes his profit, the stochastic urban model is formulated for describing the land use change. This model shows that land use change of the whole city becomes a Markov-type stochastic process.Next, introducing the quantity named F-function that characterizes stochastic urban model, it is clarified that the F-function converges the land use of the city to the condition of the fact minimally.On the basis of the above fact, following results are shown. 1) There is a kind of catastrophe phenomena in which state transition greatly changes in the slight difference of the parameter by the land use change process, and it greatly influences regulation and induction strategy. 2) It was proven that the urban area is separated naturally to high region and low region further tan the average land-use ratio. 3) It can be proven that appearance probability of land-use state increases as a condition in which the land-use continuity index is large ; hence, it was shown that the land-use continuity rose on the city naturally. 4) The analysis by stochastic urban model on the land-use change in the reconstruction process after it destroyed the city in earthquakes, and confused the land-use pattern shows that urban land-use pattern is naturally restored to the condition before the disaster.In addition, the functional form of the space correlation function indicating the correlation between land-use of two sites is deduced from the stochastic urban model. The suitability of this theoretical formula and real data often showed the possibility of the parameter estimation of the model from this correspondence.Finally, though it has argued the cases when the land use types are the two kinds for the easiness of the analysis, we expand the model to the case in which the number of land-use types is greater than two, and show that the theoretical conclusions can be generalized.