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 -