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November 2017 Guided proposals for simulating multi-dimensional diffusion bridges
Moritz Schauer, Frank van der Meulen, Harry van Zanten
Bernoulli 23(4A): 2917-2950 (November 2017). DOI: 10.3150/16-BEJ833

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.

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Moritz Schauer. Frank van der Meulen. Harry van Zanten. "Guided proposals for simulating multi-dimensional diffusion bridges." Bernoulli 23 (4A) 2917 - 2950, November 2017. https://doi.org/10.3150/16-BEJ833

Information

Received: 1 September 2014; Revised: 1 October 2015; Published: November 2017
First available in Project Euclid: 9 May 2017

zbMATH: 06778261
MathSciNet: MR3648050
Digital Object Identifier: 10.3150/16-BEJ833

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

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Vol.23 • No. 4A • November 2017
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