Research On Air Quality Index Based On Stochastic Differential Equation

With the development of China’s economy,the problem of air pollution is becoming more and more serious,which affects people’s health and daily activities.Therefore,it is of great significance to study air quality index(AQI)by using mathematical models.At first,this paper presents a stochastic differential equation to describe the dynamics of the AQI.The Euler-Maruyama algorithm could be used to discretize the stochastic differential equation.Based on the data of Wuhan AQI from 2014 to 2017,the parameters of this equation are obtained by maximum likelihood estimation,and then simulate the air quality index for the next two years.Then,the diffusion term of stochastic differential equation is generalized,and it is proved that the equation has a unique global positive solution under certain conditions.And the parameters of this equation are estimated by using the generalized moment estimation,the AQI of the next two years is simulated.On this basis,a periodic function is introduced into the drift term of the stochastic differential equation.It is proved that under some conditions,this equation still has a unique global positive solution.After discretizing the equation,the parameters are estimated by the generalized moment estimation,and the AQI of the next two years is simulated.Finally,by comparing the simulated value with the actual value,the third stochastic differential model is more effective in describing the AQI.