A Parameter Estimation Method For The Variance Of Random Terms Of Stochastic Differential Equations

At present,stochastic differential equations have been widely used in economic,physical,biological and other fields.The introduction of stochastic differential equations not only supplements the deficiencies of deterministic models,but also more accurately reflects the laws of the nature of these phenomena.The parameter estimation problem of stochastic differential equations is an important part of the research of stochastic differential equations.The application of stochastic differential equations is of great significance.Firstly,this paper uses the sample data to estimate the standard deviation of random items in stochastic differential equations by least squares method,and numerically simulates the method.The simulation results show that the estimated standard deviation of random items is smaller when the time is smaller.The smaller the error,the lower standard deviation of the random term is 0.0291,0.1206,0.1119,0.7449,when ?t=0.1,0.2,03,0.5,which means that the method is feasible when it is small.Secondly,the estimation method of the standard deviation of random items in stochastic differential equations is given by the ridge estimation method,and the numerical simulation of the method is carried out.The simulation results show that the estimated standard deviation of random items is smaller when the time is smaller.The smaller,when ?t=0.1,0.2,0.3,0.5,the standard deviation error of random items is 0.0037,0.0517,0.0351,0.0732,respectively.Under the same conditions,the estimation result of the ridge estimation is better than the least squares estimation.Finally,this paper establishes a model of combustible water content based on stochastic differential equations,and reflects the random influence of different forests on the whole water content through the standard deviation index of the stochastic water content model,and uses the sampling data of the field samples separately.The least squares estimation method and the ridge estimation method estimate the standard deviation of random items in the water content model of combustibles.The results are consistent with the actual ones,indicating that the method for estimating the standard deviation of random items in stochastic differential equations given in this paper is feasible.