Re-weighted estimation of the transition probability density for second-order diffusion processes

The transition probability density of second-order diffusion processes plays a fundamental role in statistical inference and practical applications such as financial derivatives pricing. This paper combines nonparametric Nadaraya-Watson kernel smoothing and local linear smoothing techniques to devise a re-weighted estimator for the transition probability density of second-order diffusion processes. The proposed estimator effectively addresses the persistent boundary bias inherent in Nadaraya-Watson estimation while preserving the nonnegativity constraint essential for probability densities. Under standard regularity conditions, we establish the asymptotic properties of the proposed estimator, demonstrating its theoretical superiority over existing approaches. Furthermore, Monte Carlo simulations show that the new estimator has better performance than Nadaraya-Watson estimator and local linear estimator.