Statistical estimation of diffusion processes

The aim of this training is to study various methods which can be relevant for estimating the parameters of diffusions with random drift observed with noise, at discrete times: Maximum likelihood, Bayesian estimation methods, Stochastic Approximation EM and the Gibbs sampler algorithms, Euler-Maruyama approximation method, latent auxiliary data introduced to complete the diffusion process, tuned hybrid Gibbs algorithm based on conditional Brownian bridges, simulations of the unobserved process paths, Generalized Methods of Moments (GMM). Convergence and Error bounds will also be studied. The methods will be tested on recent real datasets coming from medicine and renewal energy.

REFERENCES

Sophie Donnet and Adeline Samson (2005). Parametric estimation
for diffusion processes from discrete-time and noisy observations

ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-5809.pdf

Rubens Penha Cysne (2004). On the statistical estimation of Diffusion processes: A partial Survey. Brazilian Review of Econometrics. v. 24, n° 2, pp 273-301 Nov. 2004.

http://www.fgv.br/professor/rubens/HOMEPA GE/publica %C3 % A7 % C 3 % B 5 es/Artigos %20P ublicados/On
%20the %20Statistical%20Estimation %20of%20Diffusion %20.pdf

Helle Sorensen (2002). Parametric inference for diffusion processes observed at
discrete points in time :a survey.
http://www.econ.ku.dk/Research/Publications/pink/2002/0208.pdf