Guided proposals for simulating multi-dimensional diffusion bridges. (English) Zbl 1415.65022

Schauer, Moritz; van der Meulen, Frank; van Zanten, Harry

Bernoulli 23, No. 4A, 2917-2950 (2017).

The problem of Monte Carlo simulation of a multidimensional diffusion bridge, i.e., a diffusion conditioned to be at a specific point at a specific time in future, is considered. The actual conditional law involves the unknown density, so is unavailable for forming the proposal distribution. In view of this, a scheme is developed in order to derive a proposal distribution, in terms of an auxiliary diffusion, that can be shown to be absolutely continuous with respect to the target distribution under a set of assumptions. These assumptions are shown to hold for a class of linear diffusions. Numerical evidence in support of the proposed scheme is presented.

Reviewer: Vivek S. Borkar (Mumbai)

MSC:

65C30	Numerical solutions to stochastic differential and integral equations
60J60	Diffusion processes
65C05	Monte Carlo methods

Keywords:

multidimensional diffusion bridge; Monte Carlo simulation; proposal distribution; absolutely continuous laws

Software:

Bridge.jl