Stochastic population dynamics under regime switching II

Q. Luo, Xuerong Mao, National Natural Science Foundation of China (Funder), EPSRC (UK) (Funder), London Mathematical Society (Funder), Edinburgh Mathematical Society (Funder)

Research output: Contribution to journalArticle

75 Citations (Scopus)
152 Downloads (Pure)

Abstract

This is a continuation of our paper [Q. Luo, X. Mao, Stochastic population dynamics under regime switching, J. Math. Anal. Appl. 334 (2007) 69-84] on stochastic population dynamics under regime switching. In this paper we still take both white and color environmental noise into account. We show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population. In some special but important situations we precisely describe the limit of the average in time of the population.
Original languageEnglish
Pages (from-to)577-593
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume355
Issue number2
DOIs
Publication statusPublished - 15 Jul 2009

Fingerprint

Regime Switching
Population dynamics
Stochastic Dynamics
Population Dynamics
White noise
Color
Continuation
Upper and Lower Bounds
Sufficient

Keywords

  • brownian motion
  • markov chain
  • stochastic differential equation
  • It^o's formula
  • extinction
  • formula
  • average in time.

Cite this

Luo, Q., Mao, X., National Natural Science Foundation of China (Funder), EPSRC (UK) (Funder), London Mathematical Society (Funder), & Edinburgh Mathematical Society (Funder) (2009). Stochastic population dynamics under regime switching II. Journal of Mathematical Analysis and Applications, 355(2), 577-593. https://doi.org/10.1016/j.jmaa.2009.02.010
Luo, Q. ; Mao, Xuerong ; National Natural Science Foundation of China (Funder) ; EPSRC (UK) (Funder) ; London Mathematical Society (Funder) ; Edinburgh Mathematical Society (Funder). / Stochastic population dynamics under regime switching II. In: Journal of Mathematical Analysis and Applications. 2009 ; Vol. 355, No. 2. pp. 577-593.
@article{c5d94775e69d46cb9e4d71a9de28eabe,
title = "Stochastic population dynamics under regime switching II",
abstract = "This is a continuation of our paper [Q. Luo, X. Mao, Stochastic population dynamics under regime switching, J. Math. Anal. Appl. 334 (2007) 69-84] on stochastic population dynamics under regime switching. In this paper we still take both white and color environmental noise into account. We show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population. In some special but important situations we precisely describe the limit of the average in time of the population.",
keywords = "brownian motion, markov chain, stochastic differential equation, It^o's formula, extinction, formula, average in time.",
author = "Q. Luo and Xuerong Mao and {National Natural Science Foundation of China (Funder)} and {EPSRC (UK) (Funder)} and {London Mathematical Society (Funder)} and {Edinburgh Mathematical Society (Funder)}",
year = "2009",
month = "7",
day = "15",
doi = "10.1016/j.jmaa.2009.02.010",
language = "English",
volume = "355",
pages = "577--593",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
number = "2",

}

Luo, Q, Mao, X, National Natural Science Foundation of China (Funder), EPSRC (UK) (Funder), London Mathematical Society (Funder) & Edinburgh Mathematical Society (Funder) 2009, 'Stochastic population dynamics under regime switching II', Journal of Mathematical Analysis and Applications, vol. 355, no. 2, pp. 577-593. https://doi.org/10.1016/j.jmaa.2009.02.010

Stochastic population dynamics under regime switching II. / Luo, Q.; Mao, Xuerong; National Natural Science Foundation of China (Funder); EPSRC (UK) (Funder); London Mathematical Society (Funder); Edinburgh Mathematical Society (Funder).

In: Journal of Mathematical Analysis and Applications, Vol. 355, No. 2, 15.07.2009, p. 577-593.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Stochastic population dynamics under regime switching II

AU - Luo, Q.

AU - Mao, Xuerong

AU - National Natural Science Foundation of China (Funder)

AU - EPSRC (UK) (Funder)

AU - London Mathematical Society (Funder)

AU - Edinburgh Mathematical Society (Funder)

PY - 2009/7/15

Y1 - 2009/7/15

N2 - This is a continuation of our paper [Q. Luo, X. Mao, Stochastic population dynamics under regime switching, J. Math. Anal. Appl. 334 (2007) 69-84] on stochastic population dynamics under regime switching. In this paper we still take both white and color environmental noise into account. We show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population. In some special but important situations we precisely describe the limit of the average in time of the population.

AB - This is a continuation of our paper [Q. Luo, X. Mao, Stochastic population dynamics under regime switching, J. Math. Anal. Appl. 334 (2007) 69-84] on stochastic population dynamics under regime switching. In this paper we still take both white and color environmental noise into account. We show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population. In some special but important situations we precisely describe the limit of the average in time of the population.

KW - brownian motion

KW - markov chain

KW - stochastic differential equation

KW - It^o's formula

KW - extinction

KW - formula

KW - average in time.

UR - http://dx.doi.org/10.1016/j.jmaa.2006.12.032

U2 - 10.1016/j.jmaa.2009.02.010

DO - 10.1016/j.jmaa.2009.02.010

M3 - Article

VL - 355

SP - 577

EP - 593

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -

Luo Q, Mao X, National Natural Science Foundation of China (Funder), EPSRC (UK) (Funder), London Mathematical Society (Funder), Edinburgh Mathematical Society (Funder). Stochastic population dynamics under regime switching II. Journal of Mathematical Analysis and Applications. 2009 Jul 15;355(2):577-593. https://doi.org/10.1016/j.jmaa.2009.02.010