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

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

SN - 1201-3390

IS - 5a

ER -