Stochastic Urban Model of Land-use Pattern Formation

首先，在每个居民利益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的随机过程。其次，引入表征随机城市模型的数量F-函数，阐明了F-函数使城市的土地利用最小程度地收敛于实际情况。1)土地利用变化过程中，状态转移因参数的细微差别而发生较大变化的突变现象，极大地影响了调控和诱导策略。2)论证了城区自然分为高、低两个区域，进一步降低了平均土地利用比。3)土地利用连续性指数越大，出现土地利用状态的概率越大，说明城市土地利用的连续性自然提高。4)利用随机城市模型对地震摧毁城市后重建过程中的土地利用变化进行了分析，并对土地利用模式进行了混淆，得出了城市土地利用模式自然恢复到灾前状态，并由随机城市模型推导出了反映两地土地利用相关性的空间关联函数的函数形式。该理论公式与实际数据的适合性往往说明了模型参数估计的可能性。最后，为了便于分析，虽然对土地利用类型为两种的情况进行了论证，但将模型推广到土地利用类型数大于两种的情况，说明理论结论具有一定的推广性。

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.