Parameter estimation and random number generation for student Lévy processes

To address the challenges in estimating parameters of the widely applied Student-Levy process, the study introduces two distinct methods: a likelihood -based approach and a data -driven approach. A two-step quasi -likelihood -based method is initially proposed, countering the nonclosed nature of the Student-Levy process's distribution function under convolution. This method utilizes the limiting properties observed in high -frequency data, offering estimations via a quasilikelihood function characterized by asymptotic normality. Additionally, a novel neural -networkbased parameter estimation technique is advanced, independent of high -frequency observation assumptions. Utilizing a CNN-LSTM framework, this method effectively processes sparse, local jump -related data, extracts deep features, and maps these to the parameter space using a fully connected neural network. This innovative approach ensures minimal assumption reliance, end -to -end processing, and high scalability, marking a significant advancement in parameter estimation techniques. The efficacy of both methods is substantiated through comprehensive numerical experiments, demonstrating their robust performance in diverse scenarios.