Simulation of elliptic and hypo-elliptic conditional diffusions
Journal article, 2020

Suppose X is a multidimensional diffusion process. Assume that at time zero the state of X is fully observed, but at time 0$ ]]> only linear combinations of its components are observed. That is, one only observes the vector for a given matrix L. In this paper we show how samples from the conditioned process can be generated. The main contribution of this paper is to prove that guided proposals, introduced in [35], can be used in a unified way for both uniformly elliptic and hypo-elliptic diffusions, even when L is not the identity matrix. This is illustrated by excellent performance in two challenging cases: a partially observed twice-integrated diffusion with multiple wells and the partially observed FitzHugh-Nagumo model.

Monte Carlo method

partially observed diffusion

FitzHugh-Nagumo model

Diffusion bridge

guided proposal

Langevin sampler

twice-integrated diffusion


Joris Bierkens

Free University of Amsterdam

Frank van der Meulen

Delft University of Technology

Moritz Schauer

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Advances in Applied Probability

0001-8678 (ISSN) 1475-6064 (eISSN)

Vol. 52

Subject Categories


Probability Theory and Statistics



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