非均质空间动态随机扩散的一般方程及其应用

STOCHASTIC MOVEMENT EQUATION OF DYNAMIC SPATIAL DIFFUSION IN NONHOMOGENEOUS SPACE AND ITS APPLICATION

通过非均质空间条件下革新随机游动扩散模式的理论推导，结合实证研究成果，建立了非均质空间动态随机扩散方程。同时，将此方程应用于城市基准地价评估。

Any spatial diffusion process is a time and dependent process. A spatial diffusion has its regularities of time and space. Since T. Hagerstrand originated the time space analysis, the theories on spatial diffusion have been developed. But, the nonhomogeneous dynamic spatial diffusion has not been solved satisfactorily. This paper gives a second order differential equation on the nonhomogeneous dynamic spatial diffusion based on a stochastic movement. The model of the random movement is set up for three neighour grids. On the basis of principles of the random movement, a probability equation can be obtained. With expanding the equation by Tayler series and taking its limit, a general partial differential equation on the spatial diffusion with time dependent can be deduced. But it is too complicated and difficult to find general solution and is only approximately analysed by the numberical method. Deriving from the studies on the spatial diffusion by Hagerstrand, a general dynamic spatical diffusion equation in the nonhomogeneous space can be resulted. Hagerstrand proved that the accumulating amounts of spatial diffusion accord with a Logistic Curve. As a diffusion has proceeded for a long time, we can find the saturated amount of diffusion from the partial differential equation. A simplified general equation on the dynamic spatial diffusion in nonhomogeneous space can be resulted from taking the saturated amount into a Logistic Curve. Finally, we give an example applying the equation for the appraisal of land basis price in Fuyang. The computing conclusions show: as the distance to diffusion center increases or the multiple quality decreases, the difference between saturated land price and instantaneous amount increases. In about two months, most of plots of the city can reach their saturated land price.