Estimation in Discretely Observed Diffusions Killed at a Threshold

Estimation in discretely observed diffusions killed at a threshold

Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modeled as discretely observed diffusions which are killed when the threshold is reached. Statisti...

Estimation for Discretely Observed Diffusions using Transform Functions

This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to estimate the parameters of affine diffusions...

Quasi-maximum Likelihood Estimation of Discretely Observed Diffusions∗

This paper introduces quasi-maximum likelihood estimator for discretely observed diffusions when a closed-form transition density is unavailable. Higher order Wagner-Platen strong approximation is used to derive the first two conditional moments and a normal density function is used in estimation. Simulation study shows that the proposed estimator has high numerical precision and good numerical...

Discretely Observed Diffusions: Approximation of the Continuous-time Score Function

Consistent nonparametric Bayesian inference for discretely observed scalar diffusions

FRANK VAN DER MEULEN1 and HARRY VAN ZANTEN2 1Delft Institute of Applied Mathematics (DIAM), Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands. E-mail: [email protected] 2Department of Mathematics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: j....