Exact simulation of diffusions and new inference methods for discrete time data : also included, the one-shot CFTP algorithms

Our research began by studying the Perfect Simulation idea developed by Propp and Wilson. In Article 1 we present the “One-Shot CFTP” framework, a general Perfect Simulation algorithm that constructs a Markov chain with a given target density as its equilibrium density and then carries out Perfect Simulation on this chain. The method is based on the Read-Once CFTP idea of Wilson and the Gibbs sampler. It synthesises coupling methods having appeared in the literature but also involves a new coupling technique we have developed and which we call the “Monotone Independence Coupler”. We apply the One-Shot CFTP idea to a family of truncated gaussian densities and demonstrate its computational efficiency even in high dimensions. We then tried to apply Perfect Simulation ideas in the context of diffusion processes. Yet, the algorithm we came up with, termed the “Exact Algorithm” (EA), is based simply on rejection sampling. EA, when applicable, returns complete paths of a diffusion process through an accept/reject mechanism with Brownian path candidates. In Article 2 we present its initial version. We later managed to simplify the algorithm and to weaken considerably its conditions. The improved algorithms appear as EA1 and EA2 in Article 3 and EA3 in Article 6. In Article 6 we also present an algorithm for the exact simulation of Brownian motion hitting times for arbitrary one-sided smooth boundaries. We exploit the properties of EA to carry out parametric inference for discretely observed diffusion processes. We present methods for the unbiased estimation of