Asymptotic likelihood theory for diffusion processes

Key Points

• The aim is to explore the large-sample behavior of maximum likelihood estimates for diffusion processes.
• Investigated maximum likelihood estimates (MLE's) of diffusion process parameters.
• Analyzed results using limit normal distribution and chi-squared likelihood ratio test.
• Applied a central limit theorem for stochastic integrals to derive findings.
• MLE's converge to a limit normal distribution as sample size increases.
• An asymptotic chi-squared likelihood ratio test is established that aligns with classical asymptotic likelihood results.