Mao, Xuerong (2011) *Stationary distribution of stochastic population systems.* Systems and Control Letters, 60 (6). pp. 398-405. ISSN 0167-6911

## Abstract

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.

Item type: | Article |
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ID code: | 36921 |

Keywords: | Brownian motion, stochastic differential equation, Ito's formula, stationary distribution, Probabilities. Mathematical statistics, Mechanical Engineering, Control and Systems Engineering, Electrical and Electronic Engineering, Computer Science(all) |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Pure Administrator |

Date Deposited: | 20 Jan 2012 15:17 |

Last modified: | 27 Mar 2014 09:55 |

URI: | http://strathprints.strath.ac.uk/id/eprint/36921 |

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