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)

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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

Keywords

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

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