We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling methods, the new approach generalizes a previously...

With a view to likelihood inference for discretely observed diffusion type models, we propose a simple method of simulating approximations to diffusion bridges. The method is applicable to all one-dimensional diffusion processes and has the advantage that simple simulation methods like the Euler...

The Pearson diffusions is a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. Explicit optimal martingale estimating func- tions are found, and the...

A review is given of parametric estimation methods for discretely sampled multivariate diffusion processes. The main focus is on estimating functions and asymptotic results. Maximum likelihood estimation is briefly considered, but the emphasis is on computationally less demanding martingale...

The general theory of prediction-based estimating functions for stochastic process models is reviewed and extended. Particular attention is given to optimal estimation, asymptotic theory and Gaussian processes. Several examples of applications are presented. In particular partial observation of...

A general theory of efficient estimation for ergodic diffusions sampled at high fre- quency is presented. High frequency sampling is now possible in many applications, in particular in finance. The theory is formulated in term of approximate martingale estimating functions and covers a large...

By an application of the theory of optimal estimating function, optimal instruments for dynamic models with conditional moment restrictions are derived. The general efficiency bound is provided, along with estimators attaining the bound. It is demonstrated that the optimal estimators are always...

We propose a method for obtaining maximum likelihood estimates of parameters in diffusion models when the data is a discrete time sample of the integral of the process, while no direct observations of the process itself are available. The data are, moreover, assumed to be contaminated by...