Asymptotic properties of stochastic population dynamics

Sulin Pang; Feiqi Deng; Xuerong Mao; EPSRC (U.K.) (Funder); National Natural Science Foundation of China (Funder); Key Programs of Science and Technology of Guangzhou (Funder); Jinan University of China (Funder)

Asymptotic properties of stochastic population dynamics

Sulin Pang, Feiqi Deng, Xuerong Mao, EPSRC (U.K.) (Funder), National Natural Science Foundation of China (Funder), Key Programs of Science and Technology of Guangzhou (Funder), Jinan University of China (Funder)

Mathematics And Statistics

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Abstract

In this paper we stochastically perturb the classical Lotka{Volterra model x_ (t) = diag(x1(t); ; xn(t))[b + Ax(t)] into the stochastic dierential equation dx(t) = diag(x1(t); ; xn(t))[(b + Ax(t))dt + dw(t)]: The main aim is to study the asymptotic properties of the solution. It is known (see e.g. [3, 20]) if the noise is too large then the population may become extinct with probability one. Our main aim here is to nd out what happens if the noise is relatively small. In this paper we will establish some new asymptotic properties for the moments as well as for the sample paths of the solution. In particular, we will discuss the limit of the average in time of the sample paths.

Original language	English
Pages (from-to)	603-620
Number of pages	18
Journal	Dynamics of Continuous Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume	15
Issue number	5a
Publication status	Published - 2008

Keywords

brownian motion
stochastic dierential equation
it^o's formula
average in time
boundedness

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Pang, S., Deng, F., Mao, X., EPSRC (U.K.) (Funder), National Natural Science Foundation of China (Funder), Key Programs of Science and Technology of Guangzhou (Funder), & Jinan University of China (Funder) (2008). Asymptotic properties of stochastic population dynamics. Dynamics of Continuous Discrete and Impulsive Systems Series A: Mathematical Analysis, 15(5a), 603-620.

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title = "Asymptotic properties of stochastic population dynamics",

abstract = "In this paper we stochastically perturb the classical Lotka\{Volterra model x\_ (t) = diag(x1(t); ; xn(t))[b + Ax(t)] into the stochastic dierential equation dx(t) = diag(x1(t); ; xn(t))[(b + Ax(t))dt + dw(t)]: The main aim is to study the asymptotic properties of the solution. It is known (see e.g. [3, 20]) if the noise is too large then the population may become extinct with probability one. Our main aim here is to nd out what happens if the noise is relatively small. In this paper we will establish some new asymptotic properties for the moments as well as for the sample paths of the solution. In particular, we will discuss the limit of the average in time of the sample paths.",

keywords = "brownian motion, stochastic dierential equation, it\textasciicircum{}o's formula, average in time, boundedness",

author = "Sulin Pang and Feiqi Deng and Xuerong Mao and \{EPSRC (U.K.) (Funder)\} and \{National Natural Science Foundation of China (Funder)\} and \{Key Programs of Science and Technology of Guangzhou (Funder)\} and \{Jinan University of China (Funder)\}",

year = "2008",

language = "English",

volume = "15",

pages = "603--620",

journal = "Dynamics of Continuous Discrete and Impulsive Systems Series A: Mathematical Analysis",

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number = "5a",

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Pang, S, Deng, F, Mao, X, EPSRC (U.K.) (Funder), National Natural Science Foundation of China (Funder), Key Programs of Science and Technology of Guangzhou (Funder) & Jinan University of China (Funder) 2008, 'Asymptotic properties of stochastic population dynamics', Dynamics of Continuous Discrete and Impulsive Systems Series A: Mathematical Analysis, vol. 15, no. 5a, pp. 603-620.

TY - JOUR

T1 - Asymptotic properties of stochastic population dynamics

AU - Pang, Sulin

AU - Deng, Feiqi

AU - Mao, Xuerong

AU - EPSRC (U.K.) (Funder)

AU - National Natural Science Foundation of China (Funder)

AU - Key Programs of Science and Technology of Guangzhou (Funder)

AU - Jinan University of China (Funder)

PY - 2008

Y1 - 2008

N2 - In this paper we stochastically perturb the classical Lotka{Volterra model x_ (t) = diag(x1(t); ; xn(t))[b + Ax(t)] into the stochastic dierential equation dx(t) = diag(x1(t); ; xn(t))[(b + Ax(t))dt + dw(t)]: The main aim is to study the asymptotic properties of the solution. It is known (see e.g. [3, 20]) if the noise is too large then the population may become extinct with probability one. Our main aim here is to nd out what happens if the noise is relatively small. In this paper we will establish some new asymptotic properties for the moments as well as for the sample paths of the solution. In particular, we will discuss the limit of the average in time of the sample paths.

AB - In this paper we stochastically perturb the classical Lotka{Volterra model x_ (t) = diag(x1(t); ; xn(t))[b + Ax(t)] into the stochastic dierential equation dx(t) = diag(x1(t); ; xn(t))[(b + Ax(t))dt + dw(t)]: The main aim is to study the asymptotic properties of the solution. It is known (see e.g. [3, 20]) if the noise is too large then the population may become extinct with probability one. Our main aim here is to nd out what happens if the noise is relatively small. In this paper we will establish some new asymptotic properties for the moments as well as for the sample paths of the solution. In particular, we will discuss the limit of the average in time of the sample paths.

KW - brownian motion

KW - stochastic dierential equation

KW - it^o's formula

KW - average in time

KW - boundedness

UR - http://www.watam.org/A/index.html

M3 - Article

SN - 1201-3390

VL - 15

SP - 603

EP - 620

JO - Dynamics of Continuous Discrete and Impulsive Systems Series A: Mathematical Analysis

JF - Dynamics of Continuous Discrete and Impulsive Systems Series A: Mathematical Analysis

IS - 5a

ER -

Asymptotic properties of stochastic population dynamics

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Keywords

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