Continious-time Importance Sampling: Monte Carlo Methods which Avoid Time-discretisation Error

TL;DR

This paper introduces a continuous-time importance sampling algorithm that eliminates discretisation errors and enables unbiased online estimation for diffusions, broadening the scope of error-free Monte Carlo methods.

Contribution

It develops a new CIS algorithm that removes the need for path space work and relaxes conditions compared to existing methods like EA.

Findings

Eliminates time-discretisation errors in Monte Carlo simulations.

Provides unbiased online estimation for a broad class of diffusions.

Extends the applicability of error-free MC methods beyond previous limitations.

Abstract

In this paper we develop a continuous-time sequential importance sampling (CIS) algorithm which eliminates time-discretisation errors and provides online unbiased estimation for continuous time Markov processes, in particular for diffusions. Our work removes the strong conditions imposed by the EA and thus extends significantly the class of discretisation error-free MC methods for diffusions. The reason that CIS can be applied more generally than EA is that it no longer works on the path space of the SDE. Instead it uses proposal distributions for the transition density of the diffusion, and proposal distributions that are absolutely continuous with respect to the true transition density exist for general SDEs.