A Stochastic SIS Epidemic Model with Ornstein-Uhlenbeck Process and Brown Motion

This paper studies a stochastic differential equation SIS epidemic model, disturbed randomly by the mean-reverting Ornstein-Uhlenbeck process and Brownian motion. We prove the existence and uniqueness of the positive global solutions of the model and obtain the controlling conditions for the extinction and persistence of the disease. The results show that when the basic reproduction number Rs0 < 1, the disease will extinct, on the contrary, when the basic reproduction number Rs0 > 1, the disease will persist. Furthermore, we can inhibit the outbreak of the disease by increasing the intensity of volatility or decreasing the speed of reversion ϑ, respectively. Finally, we give some numerical examples to verify these results.

TRAJECTORY SIMULATION OF BADMINTON ROBOT BASED ON FRACTAL BROWN MOTION

This paper focuses on the design of badminton robots, and designs high-precision binocular stereo vision synchronous acquisition system hardware and multithreaded acquisition programs to ensure the left and right camera exposure synchronization and timely reading of data. Aiming at specific weak moving targets, a shape-based Brown motion model based on dynamic threshold adjustment based on singular value decomposition is proposed, and a discriminative threshold is set according to the similarity between the background and the foreground to improve detection accuracy. The three-dimensional trajectory points are extended by Kalman filter and the kinematics equation of badminton is established. The parameters of the kinematics equation of badminton are solved by the method of least squares. Based on the fractal Brownian motion algorithm, a real-time robot pose estimation algorithm is proposed to realize the real-time accurate pose estimation of the robot. A PID control model for the badminton robot executive mechanism is established between the omnidirectional wheel speed and the robot’s translation and rotation movements to achieve the precise movement of the badminton robot. All the algorithms can meet the system’s requirements for real-time performance, realize the badminton robot’s simple hit to the ball, and prospect the future research direction.

PERSAMAAN DIFERENSIAL ORNSTEIN-UHLENBECK DALAM PERAMALAN HARGA SAHAM

Geometric Brownian motion is one of the most widely used stock price model. One of the assumptions that is filled with stock return volatility is constant. Gamma Ornstein-Uhlenbeck process a model to describe volatility in finance. Additionally, Gamma Ornstein-Uhlenbeck process driven by Background Driving Levy Process (BDLP) compound Poisson process and the marginal law of volatility follows a Gamma distribution. Barndorff-Nielsen and Shepard (BNS) Gamma Ornstein-Uhlenbeck model can to sample the process for the stock price with volatility follows Gamma Ornstein-Uhlenbeck process. Based on these, the simulation result are compared BNS Gamma Ornstein-Uhlenbeck model with geometric Brown motion for Standard and Poor (SP) 500 stock data. Simulation result give BNS Gamma Ornstein-Uhlenbeck model and Geometric Brownian motion a Root Mean Square Error (RMSE) are 0,13 and 0,24 respectively. These result indicate that the BNS Gamma Ornstein-Uhlenbeck model gives a more accurate than Geometric Brownian motion