Conditioning diffusions with respect to partial observations

Jean-Louis Marchand (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we prove a result of equivalence in law between a diffusion conditioned with respect to partial observations and an auxiliary process. By partial observations we mean coordinates (or linear transformation) of the process at a finite collection of deterministic times. Apart from the theoritical interest, this result allows to simulate the conditioned diffusion through Monte Carlo's method, using the fact that the auxiliary process is easy to simulate.

Mots clés: Conditioned diffusion; Partial observations; simulation

Domaines: Probabilités [math.PR]

Jean-Louis Marchand. Conditioning diffusions with respect to partial observations. 2011. ⟨hal-00591374⟩