### Abstract

Language | English |
---|---|

Pages | 398-405 |

Number of pages | 8 |

Journal | Systems and Control Letters |

Volume | 60 |

Issue number | 6 |

Early online date | 7 Apr 2011 |

DOIs | |

Publication status | Published - Jun 2011 |

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### Keywords

- Brownian motion
- stochastic differential equation
- Ito's formula
- stationary distribution

### Cite this

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*Systems and Control Letters*, vol. 60, no. 6, pp. 398-405. https://doi.org/10.1016/j.sysconle.2011.02.013

**Stationary distribution of stochastic population systems.** / Mao, Xuerong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Stationary distribution of stochastic population systems

AU - Mao, Xuerong

PY - 2011/6

Y1 - 2011/6

N2 - In this paper we consider the stochastic differential equation (SDE) population model dx(t) = diag(x1(t), . . . , xn(t))[(b + Ax(t))dt + σdB(t)] for n interacting species. The main aim is to study the stationary distribution of the solution. It is known (see e.g. Bahar and Mao (2004) [2] and Mao (2005) [6]) if the noise intensity is sufficiently large then the population may become extinct with probability one. Our main aim here is to find out what happens if the noise is relatively small. In this paper we will show the existence of a unique stationary distribution. We will then develop a useful method to compute the mean and variance of the stationary distribution. Computer simulations will be used to illustrate our theory.

AB - In this paper we consider the stochastic differential equation (SDE) population model dx(t) = diag(x1(t), . . . , xn(t))[(b + Ax(t))dt + σdB(t)] for n interacting species. The main aim is to study the stationary distribution of the solution. It is known (see e.g. Bahar and Mao (2004) [2] and Mao (2005) [6]) if the noise intensity is sufficiently large then the population may become extinct with probability one. Our main aim here is to find out what happens if the noise is relatively small. In this paper we will show the existence of a unique stationary distribution. We will then develop a useful method to compute the mean and variance of the stationary distribution. Computer simulations will be used to illustrate our theory.

KW - Brownian motion

KW - stochastic differential equation

KW - Ito's formula

KW - stationary distribution

UR - http://www.scopus.com/inward/record.url?scp=79955810355&partnerID=8YFLogxK

U2 - 10.1016/j.sysconle.2011.02.013

DO - 10.1016/j.sysconle.2011.02.013

M3 - Article

VL - 60

SP - 398

EP - 405

JO - Systems and Control Letters

T2 - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

IS - 6

ER -