• 论文 •

### 非均质空间随机扩散方程及其在城市基准地价评估中的运用

1. 南京大学大地海洋科学系, 南京 210093
• 收稿日期:1994-06-01 修回日期:1994-11-01 出版日期:1995-05-15 发布日期:1995-05-15

### STOCHASTIC MOVEMENT EQUATION OF SPATIAL DIFFUSION IN NONHOMOGONEOUS FIELD AND ITS APPLICATION FOR THE APPRAISAL OF LAND PRICE

Shan Weidong, Bao Haosheng

1. Dept of Geo and Ocean Sciences, Nanjing University. Nanjing 210093
• Received:1994-06-01 Revised:1994-11-01 Online:1995-05-15 Published:1995-05-15

Abstract: Innovation does not diffuse identically and evenly. The diffusion process which initiates around the diffusion center is influenced by the multiple quality (m) including natural and social-economical factors and distance (x) to the center. T. Hagevstrand founded spatial diffusion theories based on MIF (Mean Information Field) in 1971. There are some problems to be further researched, such as diffusion in nonhomogeneous field and diffusion expression by a general spatial diffusion function relating to m and x. Furthermore. some reasons why basis land price can not be satisfiedly evaluated by seperating differential income are analysed.This paper theoretically imitates stochastic spatial diffusion in nonhomogoneous fields and regards the process as the movement of random grain mediums. supposing that the system of the multiple quality m and distance x consists of many single and very small checks. Innovation influence is composed of infinite and noncontinuous small grain mediums, and the volume of which is 1. The mediums seperate each other and make relative movement in the m-x system. the movement of grain mediums can be described as the random movement of grain mediums. So, the movement of a large amount of grain mediums can be expressed as a stochastic process. The model of the random movement is set up by three neighboring checks. Thus. on the basis of the principle of random movement ,we can obtain a probability equation. By expanding the equation by Taylor series and taking a limit,a general diffusion equation of parabola type is deduced. It is proved that the diffusion process accords with the Kolmogorov diffusion equation. By solving a partial differential equation, a diffusion probability density function is obtained. By making some assumptions and intergrating the density function, a general expression on the nonhomogenous spatial diffusion is obtained. It can describe the multiple influence of expansion diffusion, hierarchic diffusion and relocation diffusion.The principle of defining parameters and the approximatly computing methodes of Gauss complement function is given. Some methodes are also recommended. The best one is Marquardt algorithm for least-squares estimation of nonlinear parameters.By means of the spatial diffusion equation, the main problems in the appraisal of basis land price can be solved. Finally , an example of the basis land price in Fuyang is given. The conclusion of calculations is that fitting error equals + 9 Yuan/m2 and maximum curve fitting error equals 24Yuan/m2.

• F293.3