Temperature Stochastic Model With Adding Tempered Fractional Brownian Motion Noise

The stochastic model describing temperature develops from the initial Brownian motion to the fractional Brownian motion.In this paper,we use the response to low-frequency data of parameter ? in the tempered fractional Brownian motion to optimize the temperature stochastic model,and give the determination method to all parameter and some simulations to show the superiority of our model.Compare with other models we find that the performance of fractional Brownian motion and Gaussian color noise under 0.6 times filter are the best,and the tempered fractional Brownian motion is even better.In addition,based on the first-level geographical divisions of China we select seven cities for simulation.Finally,inspired by the literature[13],we introduce another stochastic integral model—Tempered fractional integral model.