Wavelet analysis for the solution to the wave equation with fractional noise in time and white noise in space

Abstract

Via Malliavin calculus, we analyze the limit behavior in distribution of the spatial wavelet variation for the solution to the stochastic linear wave equation with fractional Gaussian noise in time and white noise in space. We propose a wavelet-type estimator for the Hurst parameter of the this solution and we study its asymptotic properties.

Intelligent prediction of capacity margin in different time periods based on wavelet analysis

“…Wavelet analysis is a useful tool for signal analysis that is utilized extensively in numerous fields like image analysis and signal processing. The market's supply-demand relationship determines electricity prices, but at the same time, there are various complex factors that affect electricity prices, such as unpredictable factors such as power generation games and equipment failures, which endow electricity prices with more high-frequency and detailed components, resulting in electricity prices deviating from normal values and concealing the true changing rules of electricity prices, which is not conducive to accurate prediction of electricity prices [10]. The author uses wavelet decomposition technology to extract the approximate components of the electricity price sequence, thereby eliminating the high-frequency components in the electricity price sequence, and trains the neural network using the approximate components as the historical electricity price of the neural network.…”