Guided proposals for simulating multi-dimensional diffusion bridges

Moritz Schauer, Frank Van Der Meulen, Harry Van Zanten

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)
16 Downloads (Pure)

Abstract

A Monte Carlo method for simulating a multi-dimensional diffusion process conditioned on hitting a fixed point at a fixed future time is developed. Proposals for such diffusion bridges are obtained by superimposing an additional guiding term to the drift of the process under consideration. The guiding term is derived via approximation of the target process by a simpler diffusion processes with known transition densities. Acceptance of a proposal can be determined by computing the likelihood ratio between the proposal and the target bridge, which is derived in closed form.We show under general conditions that the likelihood ratio is well defined and show that a class of proposals with guiding term obtained from linear approximations fall under these conditions.
Original languageEnglish
Pages (from-to)2917-2950
Number of pages34
JournalBernoulli: a journal of mathematical statistics and probability
Volume23
Issue number4A
DOIs
Publication statusPublished - 2017

Keywords

  • Change of measure
  • Data augmentation
  • Linear processes
  • Multidimensional diffusion bridge

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