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Journal of Advanced Transportation
Volume 2017 (2017), Article ID 4013875, 8 pages
Research Article

Analysis and Prediction on Vehicle Ownership Based on an Improved Stochastic Gompertz Diffusion Process

1Institute of Transportation Engineering, Tsinghua University, Beijing 100084, China
2College of Metropolitan Transportation, Beijing University of Technology, Beijing 100124, China
3School of Architecture and Urban Planning, Beijing University of Civil Engineering and Architecture, Beijing, China

Correspondence should be addressed to He Ma; nc.ude.auhgnist.sliam@31ham

Received 19 December 2016; Revised 19 April 2017; Accepted 27 April 2017; Published 11 July 2017

Academic Editor: Guohui Zhang

Copyright © 2017 Huapu Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper aims at introducing a new improved stochastic differential equation related to Gompertz curve for the projection of vehicle ownership growth. This diffusion model explains the relationship between vehicle ownership and GDP per capita, which has been studied as a Gompertz-like function before. The main innovations of the process lie in two parts: by modifying the deterministic part of the original Gompertz equation, the model can present the remaining slow increase when the S-shaped curve has reached its saturation level; by introducing the stochastic differential equation, the model can better fit the real data when there are fluctuations. Such comparisons are carried out based on data from US, UK, Japan, and Korea with a time span of 1960–2008. It turns out that the new process behaves better in fitting curves and predicting short term growth. Finally, a prediction of Chinese vehicle ownership up to 2025 is presented with the new model, as China is on the initial stage of motorization with much fluctuations in growth.