Simulation of elliptic and hypo-elliptic conditional diffusions

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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 languageEnglish
Pages (from-to)173-212
Number of pages40
JournalAdvances in Applied Probability
Volume52
Issue number1
DOIs
Publication statusPublished - 2020

Keywords

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

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