No abstract

The stochastic differential equation (SDE) has been used to model various phenomena and investigate their properties. Conditional moments of stochastic processes can be used to price financial derivatives whose payoffs depend on conditional moments of underlying assets. In general, the transition probability density function (PDF) of a stochastic process is often unavailable in closed form. Thus, the conditional moments, which can be directly computed by applying the transition PDFs, may be unavailable in closed form. In this work, we studied an inhomogeneous nonlinear drift constant elasticity of variance (IND-CEV) process, which is a class of diffusions that have time-dependent parameter functions; therefore, their sample paths are asymmetric. The closed-form formulas for conditional moments of the IND-CEV process were derived without having a condition on eigenfunctions or the transition PDF. The analytical results were examined through Monte Carlo simulations.

The smart city concept has been popularized in the urbanization of major metropolitan areas through the implementation of intelligent systems and technology to serve the increasing human population. This work developed an automatic light adjustment system at Thammasat University, Rangsit Campus, Thailand, with a primary objective of optimizing energy efficiency, while providing sufficient illumination for the campus. The development consists of two sections: the device control and the prediction model. The device control functionalities were developed with the user interface to enable control of the smart street light devices and the application programming interface (API) to send the light-adjusting command. The prediction model was created using an AI-assisted data analytic platform to obtain the predicted illuminance values so as to, subsequently, suggest light-dimming values according to the current environment. Four machine-learning models were performed on a nine-month environmental dataset to acquire predictions. The result demonstrated that the three-day window size setting with the XGBoost model yielded the best performance, attaining the correlation coefficient value of 0.922, showing a linear relationship between actual and predicted illuminance values using the test dataset. The prediction retrieval API was established and connected to the device control API, which later created an automated system that operated at a 20-min interval. This allowed real-time feedback to automatically adjust the smart street lighting devices through the purpose-designed data analytics features.