Insider Trading with Memory under Random Deadline

In this paper, we study a model of continuous-time insider trading in which noise traders have some memories and the trading stops at a random deadline. By a filtering theory on fractional Brownian motion and the stochastic maximum principle, we obtain a necessary condition of the insider’s optimal strategy, an equation satisfied. It shows that when the volatility of noise traders is constant and the noise traders’ memories become weaker and weaker, the optimal trading intensity and the corresponding residual information tend to those, respectively, when noise traders have no any memory. And, numerical simulation illustrates that if both the trading intensity of the insider and the volatility of noise trades are independent of trading time, the insider’s expected profit is always lower than that when the asset value is disclosed at a finite fixed time; this is because the trading time ahead is a random deadline which yields the loss of the insider’s information.

A Wavelet Threshold Function for Treatment of Partial Discharge Measurements

Based on the wavelet transform filtering theory, the chapter will describe the elaboration of a wavelet threshold function intended for the denoising of the partial discharge phenomenon measurements. This new function, conveniently named Fleming threshold, is based on the logistic function, which is well known for its utility in several important areas. In the development is shown some variations in the application of the Fleming function, in an attempt to identify the decomposition levels where the thresholding process must be more stringent and those where it can be more lenient, which increases its effectiveness in the removal of noisy coefficients. The proposed function and its variants demonstrate excellent results compared to other wavelet thresholding methods already described in the literature, including the famous Hard and Soft functions.

Kalman Filtering Applied to Induction Motor State Estimation

This chapter presents a full definition and explanation of Kalman filtering theory, precisely the filter stochastic algorithm. After the definition, a concrete example of application is explained. The simulated example concerns an extended Kalman filter applied to machine state and speed estimation. A full observation of an induction motor state variables and mechanical speed will be presented and discussed in details. A comparison between extended Kalman filtering and adaptive Luenberger state observation will be highlighted and discussed in detail with many figures. In conclusion, the chapter is ended by listing the Kalman filtering main advantages and recent advances in the scientific literature.