Simulation of elliptic and hypo-elliptic conditional diffusions

Journal article (2020)

Authors

G.N.J.C. Bierkens Vrije Universiteit Amsterdam
F.H. van der Meulen Statistics - EEMCS
M.R. Schauer University of Gothenburg, Chalmers University of Technology
Research Group
Statistics (EEMCS) (TU Delft)
Copyright: © 2020 G.N.J.C. Bierkens, F.H. van der Meulen, M.R. Schauer
DOI: https://doi.org/10.1017/apr.2019.54
Monte Carlo method Diffusion bridge FitzHugh-Nagumo model Guided proposal Partially observed diffusion Langevin sampler Twice-integrated diffusion
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Published Date

2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

Abstract

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.