Journal
ADVANCES IN APPLIED PROBABILITY
Volume 52, Issue 1, Pages 173-212Publisher
APPLIED PROBABILITY TRUST
DOI: 10.1017/apr.2019.54
Keywords
Diffusion bridge; Monte Carlo method; FitzHugh-Nagumo model; guided proposal; Langevin sampler; partially observed diffusion; twice-integrated diffusion
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Funding
- Dutch Research Council (NWO) [016, Vidi.189.043]
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Suppose X is a multidimensional diffusion process. Assume that at time zero the state of X is fully observed, but at time T > 0 only linear combinations of its components are observed. That is, one only observes the vector LXT 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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