Air Temperature Model Based On Stochastic Differential Equation

Since the concept of stochastic differential equation is proposed,it has been developed rapidly.Its application has involved many aspects including finance,physics,biology,cybernetics and so on,and has achieved good results.Since the concept of global warming and greenhouse effect has been gradually popularized,the global average temperature has been paid more and more attention.Therefore,this paper hopes to connect the two.By analyzing the correlation properties and data variation characteristics of global average temperature,the stochastic growth differential equation model of global average temperature is established.The temperature data is predicted and analyzed by combining the estimation of relevant parameters and numerical calculation.In this paper,we first select and detect the collected data to judge whether there are outliers.Then,according to the property of no aftereffect of temperature change,we establish a stochastic differential equation model.Combined with the processed global average temperature data,we found that the data showed the characteristics of continuous fluctuation and growth trend,so we established a stochastic differential growth model of global average temperature.Through the research and analysis of the solution of the equation,the expectation and variance are calculated.It is concluded that the temperature will always rise with the increase of time in this model.Obviously,this is not in line with the actual situation.Therefore,by adding retardation factor to the model,a stochastic retardation growth model of global average temperature is re established.On the basis of stochastic retarded growth model,the relevant parameters are estimated.In this paper,the parameters involved in the model are estimated.The intrinsic growth rate and white noise figure are estimated by moment estimation and maximum likelihood estimation respectively.The environmental capacity was estimated by four point average method and least square method.For the different estimation methods of two groups of parameters,the optimal combination of parameter estimation methods is selected by calculating and comparing the square sum of errors.The results show that: when the intrinsic growth rate and white noise figure choose the moment estimation method,and the environmental capacity choose the least square method,the model fitting error is the smallest,which is 1.2497.Finally,on the basis of the optimal parameters,the model is fitted,and the temperature data is simply predicted and analyzed.It is concluded that if human beings do not control it,the global average temperature will continue to increase.