Parameter Estimation Of A Type Of Mixed Fractional Brownian Motion And Its Applications

This paper mainly studies the parameter estimation of mixed fractional Brownian motion with drift term and its applications.Firstly,the maximum likelihood estimation method and the R/S method are used to estimate the unknown parameters.Then Monte Carlo method is used to demonstrate the effectiveness of the estimation method used in this paper.Finally,by using the method proposed in this paper and the obtained expression,empirical research is conducted on the Shanghai Interbank Offered Rate.Its parameter estimates are obtained,and the estimated values are used to generate the trajectory map of the mixed fractional Brownian motion with drift terms.Then this trajectory map is compared with the actual trajectory map.