Computing absorbing times via fluid approximations

Nicolas Gast 1, 2 Bruno Gaujal 1, 2
Abstract : In this paper, we compute the absorbing time Tn of a n-dimensional discrete time Markov chain made of n components, each with an absorbing state and evolving in mutual exclusion. We show that the random absorbing time Tn is well approximated by a deterministic time tn that is the first time when a fluid approximation of the chain approaches the absorbing state at a distance 1/n. We provide an asymptotic expansion of tn that uses the spectral decomposition of the kernel of the chain as well as the asymptotic distribution of Tn, relying on extreme values theory. We show the applicability of this approach with three different problems: the coupon collector, the erasure channel lifetime and the coupling times of random walks in high dimensional spaces.
Complete list of metadatas

Cited literature [22 references]  Display  Hide  Download

https://hal.inria.fr/hal-01337950
Contributor : Nicolas Gast <>
Submitted on : Monday, June 27, 2016 - 3:55:46 PM
Last modification on : Friday, October 25, 2019 - 1:32:20 AM

File

absorbingTime_GastGaujal.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01337950, version 1

Citation

Nicolas Gast, Bruno Gaujal. Computing absorbing times via fluid approximations. 2016. ⟨hal-01337950⟩

Share

Metrics

Record views

506

Files downloads

233