Simulation of elliptic and hypo-elliptic conditional diffusions-Reference-Cited by-同舟云学术

Simulation of elliptic and hypo-elliptic conditional diffusions

Published:2020-03 Issue:1 Volume:52 Page:173-212
ISSN:0001-8678
Container-title:Advances in Applied Probability
language:en
Short-container-title:Adv. Appl. Probab.

Author:

Bierkens Joris,van der Meulen Frank,Schauer Moritz

Abstract

AbstractSuppose 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

$L X_T$

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.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

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