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

This paper deals with the numerical approximation of normalizing constantsproduced by particle methods, in the general framework of Feynman-Kac sequencesof measures. It is well-known that the corresponding estimates satisfy acentral limit theorem for a fixed time horizon $n$ as the number of particles$N$ goes to infinity. Here, we study the situation where both $n$ and $N$ go toinfinity in such a way that $\lim_{n\rightarrow\infty}% n/N=\alpha>0$. In thiscontext, Pitt et al. \cite{pitt2012} recently conjectured that a lognormalcentral limit theorem should hold. We formally establish this result here,under general regularity assumptions on the model. We also discuss specialclasses of models (time-homogeneous environment and ergodic random environment)for which more explicit descriptions of the limiting bias and variance can beobtained.

A Lognormal Central Limit Theorem for Particle Approximations of Normalizing Constants