Header

UZH-Logo

Maintenance Infos

On the emergence of random initial conditions in fluid limits


Barbour, A D; Chigansky, Pavel; Klebaner, Fima (2016). On the emergence of random initial conditions in fluid limits. Journal of Applied Probability, 53(4):1193-1205.

Abstract

The paper presents a phenomenon occurring in population processes that start near zero and have large carrying capacity. By the classical result of Kurtz (1970), such processes, normalized by the carrying capacity, converge on finite intervals to the solutions of ordinary differential equations, also known as the fluid limit. When the initial population is small relative to carrying capacity, this limit is trivial. Here we show that, viewed at suitably chosen times increasing to infinity, the process converges to the fluid limit, governed by the same dynamics, but with a random initial condition. This random initial condition is related to the martingale limit of an associated linear birth and death process.

Abstract

The paper presents a phenomenon occurring in population processes that start near zero and have large carrying capacity. By the classical result of Kurtz (1970), such processes, normalized by the carrying capacity, converge on finite intervals to the solutions of ordinary differential equations, also known as the fluid limit. When the initial population is small relative to carrying capacity, this limit is trivial. Here we show that, viewed at suitably chosen times increasing to infinity, the process converges to the fluid limit, governed by the same dynamics, but with a random initial condition. This random initial condition is related to the martingale limit of an associated linear birth and death process.

Statistics

Citations

Dimensions.ai Metrics
1 citation in Web of Science®
1 citation in Scopus®
2 citations in Microsoft Academic
Google Scholar™

Altmetrics

Downloads

5 downloads since deposited on 27 Dec 2017
5 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2016
Deposited On:27 Dec 2017 15:06
Last Modified:18 Apr 2018 11:49
Publisher:Applied Probability Trust
ISSN:0021-9002
Funders:Australian Research Council
OA Status:Green
Publisher DOI:https://doi.org/10.1017/jpr.2016.74

Download

Download PDF  'On the emergence of random initial conditions in fluid limits'.
Preview
Content: Accepted Version
Language: English
Filetype: PDF
Size: 125kB
View at publisher