Simulation of elliptic and hypo-elliptic conditional diffusions

Joris Bierkens; Frank Van Der Meulen; Moritz Schauer

doi:10.1017/apr.2019.54

Simulation of elliptic and hypo-elliptic conditional diffusions

Joris Bierkens^*, Frank Van Der Meulen, Moritz Schauer

^*Corresponding author for this work

Mathematics

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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.

Original language	English
Pages (from-to)	173-212
Number of pages	40
Journal	Advances in Applied Probability
Volume	52
Issue number	1
DOIs	https://doi.org/10.1017/apr.2019.54
Publication status	Published - Mar 2020

Keywords

Diffusion bridge
FitzHugh-Nagumo model
guided proposal
Langevin sampler
Monte Carlo method
partially observed diffusion
twice-integrated diffusion

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simulation-of-elliptic-and-hypo-elliptic-conditional-diffusionsFinal published version, 2.08 MBLicence: Article 25fa Dutch Copyright Act

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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.",

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AU - Bierkens, Joris

AU - Van Der Meulen, Frank

AU - Schauer, Moritz

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Simulation of elliptic and hypo-elliptic conditional diffusions

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Keywords

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