On effects of discretization on estimators of drift parameters for diffusion processes
- Kloeden, Peter E.
- Platen, Eckhard
- Schurz, Henri
- Sørensen, Michael
2010 Mathematics Subject Classification
- 60H10 62F12 65U05
- Discrete time sampling, Inference for stochastic processes, Maximum likelihood estimation, Numerical methods, Simulation, Stochastic differential equations, Stochastic Taylor expansions
In this paper statistical properties of estimators of drift parameters for diffusion processes are studied by modern numerical methods for stochastic differential equations. This is a particularly useful method for discrete time samples, where estimators can be constructed by making discrete time approximations to the stochastic integrals appearing in the maximum likelihood estimators for continuously observed diffusions. A review is given of the necessary theory for parameter estimation for diffusion processes and for simulation of diffusion processes. Three examples are studied.