English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article we consider the filtering problem associated to partiallyobserved diffusions, with observations following a marked point process. In themodel, the data form a point process with observation times that have itsintensity driven by a diffusion, with the associated marks also depending uponthe diffusion process. We assume that one must resort to time-discretizing thediffusion process and develop particle and multilevel particle filters torecursively approximate the filter. In particular, we prove that our multilevelparticle filter can achieve a mean square error (MSE) of$\mathcal{O}(\epsilon^2)$ ($\epsilon>0$ and arbitrary) with a cost of$\mathcal{O}(\epsilon^{-2.5})$ versus using a particle filter which has a costof $\mathcal{O}(\epsilon^{-3})$ to achieve the same MSE. We then show how thismethodology can be extended to give unbiased (that is with notime-discretization error) estimators of the filter, which are proved to havefinite variance and with high-probability have finite cost. Finally, we extendour methodology to the problem of online static-parameter estimation.

Unbiased and Multilevel Methods for a Class of Diffusions Partially Observed via Marked Point Processes