# Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes

## TL;DR

This paper introduces Sequential Monte Carlo to the QMC community, extends SQMC to continuous-time diffusion models, and discusses dimension reduction techniques to maintain performance in high-dimensional filtering problems.

## Contribution

It presents a new introduction of SMC to QMC researchers, extends SQMC to diffusion processes, and explores dimension reduction for high-dimensional filtering.

## Key findings

- Successful extension of SQMC to diffusion processes
- Dimension reduction improves SQMC performance
- Enhanced understanding of SQMC in continuous-time models

## Abstract

SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. Gerber and Chopin (2015) introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose members are usually less familiar with state-space models and particle filtering; (b) to extend SQMC to the filtering of continuous-time state-space models, where the latent process is a diffusion. A recurring point in the paper will be the notion of dimension reduction, that is how to implement SQMC in such a way that it provides good performance despite the high dimension of the problem.